TSTP Solution File: SEV348^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV348^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n091.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 300.01s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV348^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n091.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 08:54:11 CDT 2014
% % CPUTime : 300.01
% 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 0xe6de60>, <kernel.Constant object at 0xe6d3b0>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0x128cea8>, <kernel.DependentProduct object at 0x104ec68>) of role type named cGVB_OP
% Using role type
% Declaring cGVB_OP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xe6d560>, <kernel.DependentProduct object at 0x104ed40>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xe6db90>, <kernel.DependentProduct object at 0x104ed88>) of role type named cGVB_OPP
% Using role type
% Declaring cGVB_OPP:(fofType->Prop)
% FOF formula ((iff (cGVB_OPP x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))) of role conjecture named cGVB_AX_OPP
% Conjecture to prove = ((iff (cGVB_OPP x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))):Prop
% We need to prove ['((iff (cGVB_OPP x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))']
% Parameter fofType:Type.
% Parameter x:fofType.
% Parameter cGVB_OP:(fofType->(fofType->fofType)).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_OPP:(fofType->Prop).
% Trying to prove ((iff (cGVB_OPP x)) ((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))
% 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 eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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 eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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 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 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 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 x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) 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)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% 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 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) 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 x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) 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)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% 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_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))):(((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found (eq_ref0 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) 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 x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))):(((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) (fun (x0:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found (eta_expansion_dep00 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) 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 x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) 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 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 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 x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: a:=x:fofType;b:=((cGVB_OP x00) x01):fofType
% Found x03 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) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% 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 x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: a:=x:fofType;b:=((cGVB_OP x00) x01):fofType
% Found x03 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) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found (x030 ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: a:=x:fofType;b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))):(((eq Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x)))
% Found (eq_ref0 (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) as proof of (((eq Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) b)
% Found ((eq_ref Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) as proof of (((eq Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) b)
% Found ((eq_ref Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) as proof of (((eq Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) b)
% Found ((eq_ref Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) as proof of (((eq Prop) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x))) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found (x030 ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))):(((eq Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))))
% Found (eq_ref0 ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) as proof of (((eq Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) b)
% Found ((eq_ref Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) as proof of (((eq Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) b)
% Found ((eq_ref Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) as proof of (((eq Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) b)
% Found ((eq_ref Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) as proof of (((eq Prop) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))))) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: a:=x:fofType;b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found (x030 ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% 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 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 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 (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% 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 eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) x)
% Found (x030 ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found ((x03 (fun (x2:fofType)=> (((eq fofType) x2) x))) ((eq_ref fofType) x)) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (((eq fofType) x) ((cGVB_OP x00) x01))):(((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))
% Found (eq_ref0 (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% Found ((eq_ref Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% Found ((eq_ref Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% Found ((eq_ref Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% 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 eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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 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 eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) 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 (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% 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 eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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 (((eq fofType) x) ((cGVB_OP x00) x01))):(((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))
% Found (eq_ref0 (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% Found ((eq_ref Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% Found ((eq_ref Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% Found ((eq_ref Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) as proof of (((eq Prop) (((eq fofType) x) ((cGVB_OP x00) x01))) b)
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% 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)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% 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 (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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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 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 x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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 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) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))->(cGVB_OPP x)))
% Found x02:(P x)
% Instantiate: b:=x:fofType
% Found x02 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_OPP x)->((ex fofType) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))))
% 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 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x02:(P x)
% Instantiate: b:=x:fofType
% Found x02 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found x02:(P0 b)
% Instantiate: b:=x:fofType
% Found (fun (x02:(P0 b))=> x02) as proof of (P0 x)
% Found (fun (P0:(fofType->Prop)) (x02:(P0 b))=> x02) as proof of ((P0 b)->(P0 x))
% Found (fun (P0:(fofType->Prop)) (x02:(P0 b))=> x02) as proof of (P b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x02:(P ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x02 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% 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 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% 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 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 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 x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% 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 eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% 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 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found x02:(P0 b)
% Instantiate: b:=x:fofType
% Found (fun (x02:(P0 b))=> x02) as proof of (P0 x)
% Found (fun (P0:(fofType->Prop)) (x02:(P0 b))=> x02) as proof of ((P0 b)->(P0 x))
% Found (fun (P0:(fofType->Prop)) (x02:(P0 b))=> x02) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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 eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x00) x01))
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Instantiate: b:=(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P))):Prop
% Found ex_ind as proof of b
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% 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_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% 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_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz)))))))
% Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% Instantiate: b:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% Found eq_sym0 as proof of b
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))):(((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) (fun (x0:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found (eta_expansion_dep00 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found x02:(P ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x02 as proof of (P0 b)
% 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 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 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 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) 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 eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x01)
% Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% Instantiate: b:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% Found eq_sym0 as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found eq_ref00:=(eq_ref0 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))):(((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found (eq_ref0 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))):(((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz)))))
% Found (eq_ref0 (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) as proof of (((eq (fofType->Prop)) (fun (Xz:fofType)=> ((and ((and (cGVB_M x00)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x00) Xz))))) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% 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 x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b)
% Found x020:(P ((cGVB_OP x00) x01))
% Found (fun (x020:(P ((cGVB_OP x00) x01)))=> x020) as proof of (P ((cGVB_OP x00) x01))
% Found (fun (x020:(P ((cGVB_OP x00) x01)))=> x020) as proof of (P0 ((cGVB_OP x00) x01))
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01))))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x02:(P x)
% Instantiate: b:=x:fofType
% Found x02 as proof of (P0 b)
% Found x020:(P ((cGVB_OP x00) x01))
% Found (fun (x020:(P ((cGVB_OP x00) x01)))=> x020) as proof of (P ((cGVB_OP x00) x01))
% Found (fun (x020:(P ((cGVB_OP x00) x01)))=> x020) as proof of (P0 ((cGVB_OP x00) x01))
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M x0)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP x0) Xz)))))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and (cGVB_M Xy)) (cGVB_M Xz))) (((eq fofType) x) ((cGVB_OP Xy) Xz))))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) x) b0)
% 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 x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x10:(P ((cGVB_OP x00) x01))
% Found (fun (x10:(P ((cGVB_OP x00) x01)))=> x10) as proof of (P ((cGVB_OP x00) x01))
% Found (fun (x10:(P ((cGVB_OP x00) x01)))=> x10) as proof of (P0 ((cGVB_OP x00) x01))
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found x03:(((eq fofType) x) ((cGVB_OP x00) x01))
% Instantiate: b:=x:fofType;b0:=((cGVB_OP x00) x01):fofType
% Found x03 as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x02:(P x)
% Instantiate: b:=x:fofType
% Found x02 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x00) x01))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% 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 ((cGVB_OP x00) x01)):(((eq fofType) ((cGVB_OP x00) x01)) ((cGVB_OP x00) x01))
% Found (eq_ref0 ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found ((eq_ref fofType) ((cGVB_OP x00) x01)) as proof of (((eq fofType) ((cGVB_OP x00) x01)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x020:(P x)
% Found (fun (x020:(P x))=> x020) as proof of (P x)
% Found (fun (x020:(P x))=> x020) as proof of (P0 x)
% 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 b):(((eq fofType) b) b)
% Found
% EOF
%------------------------------------------------------------------------------