TSTP Solution File: SEV352^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV352^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n116.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 300.05s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV352^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n116.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:55:01 CDT 2014
% % CPUTime : 300.05
% 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 0x15d0440>, <kernel.Constant object at 0x15b15f0>) of role type named z
% Using role type
% Declaring z:fofType
% FOF formula (<kernel.Constant object at 0x10c2dd0>, <kernel.Single object at 0x15b1560>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0x15d0440>, <kernel.DependentProduct object at 0x162c758>) of role type named cGVB_FIRST
% Using role type
% Declaring cGVB_FIRST:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x15d0440>, <kernel.DependentProduct object at 0x162c758>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x15b1098>, <kernel.DependentProduct object at 0x162ce60>) of role type named cGVB_OPP
% Using role type
% Declaring cGVB_OPP:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x15b1248>, <kernel.DependentProduct object at 0x162cbd8>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x15b1560>, <kernel.DependentProduct object at 0x162c440>) of role type named cGVB_DOMAIN
% Using role type
% Declaring cGVB_DOMAIN:(fofType->fofType)
% FOF formula ((iff ((cGVB_IN z) (cGVB_DOMAIN x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))) of role conjecture named cGVB_B4
% Conjecture to prove = ((iff ((cGVB_IN z) (cGVB_DOMAIN x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))):Prop
% We need to prove ['((iff ((cGVB_IN z) (cGVB_DOMAIN x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))']
% Parameter fofType:Type.
% Parameter z:fofType.
% Parameter x:fofType.
% Parameter cGVB_FIRST:(fofType->fofType).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_OPP:(fofType->Prop).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_DOMAIN:(fofType->fofType).
% Trying to prove ((iff ((cGVB_IN z) (cGVB_DOMAIN x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))):(((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found (eq_ref0 ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))):(((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found (eq_ref0 ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found 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) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))):(((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found (eq_ref0 (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))):(((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found (eq_ref0 (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) as proof of (((eq (fofType->Prop)) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) x))) (((eq fofType) z) (cGVB_FIRST x0)))))
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) x))) (((eq fofType) z) (cGVB_FIRST x0)))))
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) x))) (((eq fofType) z) (cGVB_FIRST x0)))))
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((and ((and ((and (cGVB_M x00)) (cGVB_OPP x00))) ((cGVB_IN x00) x))) (((eq fofType) z) (cGVB_FIRST x00))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) x))) (((eq fofType) z) (cGVB_FIRST x0)))))
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq 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 (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of b
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq 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 (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))
% Found iff_sym0:=(iff_sym ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))):(forall (B:Prop), (((iff ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))) B)->((iff B) ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))))
% Instantiate: b:=(forall (B:Prop), (((iff ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))) B)->((iff B) ((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))))):Prop
% Found iff_sym0 as proof of b
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN 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_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN 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) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found x10:(P z)
% Found (fun (x10:(P z))=> x10) as proof of (P z)
% Found (fun (x10:(P z))=> x10) as proof of (P0 z)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% 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 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) 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 (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))
% Found x10:(P z)
% Found (fun (x10:(P z))=> x10) as proof of (P z)
% Found (fun (x10:(P z))=> x10) as proof of (P0 z)
% Found eq_ref00:=(eq_ref0 (((eq fofType) z) (cGVB_FIRST x00))):(((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) (((eq fofType) z) (cGVB_FIRST x00)))
% Found (eq_ref0 (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found ((eq_ref Prop) (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found ((eq_ref Prop) (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found ((eq_ref Prop) (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN 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 x04:(((eq fofType) z) (cGVB_FIRST x02))
% Instantiate: a:=z:fofType;b:=(cGVB_FIRST x02):fofType
% Found x04 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found eq_ref00:=(eq_ref0 (((eq fofType) z) (cGVB_FIRST x00))):(((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) (((eq fofType) z) (cGVB_FIRST x00)))
% Found (eq_ref0 (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found ((eq_ref Prop) (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found ((eq_ref Prop) (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found ((eq_ref Prop) (((eq fofType) z) (cGVB_FIRST x00))) as proof of (((eq Prop) (((eq fofType) z) (cGVB_FIRST x00))) b)
% Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% Instantiate: a:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% Found conj as proof of a
% Found x04:(((eq fofType) z) (cGVB_FIRST x02))
% Instantiate: a:=z:fofType;b:=(cGVB_FIRST x02):fofType
% Found x04 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) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of a
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) z)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST x00)):(((eq fofType) (cGVB_FIRST x00)) (cGVB_FIRST x00))
% Found (eq_ref0 (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found x04:(((eq fofType) z) (cGVB_FIRST x02))
% Instantiate: a:=z:fofType;b:=(cGVB_FIRST x02):fofType
% Found x04 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) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) z)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST x00)):(((eq fofType) (cGVB_FIRST x00)) (cGVB_FIRST x00))
% Found (eq_ref0 (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found x04:(((eq fofType) z) (cGVB_FIRST x02))
% Instantiate: a:=z:fofType;b:=(cGVB_FIRST x02):fofType
% Found x04 as proof of (((eq fofType) a) b)
% Found x1:(P z)
% Instantiate: b:=z:fofType
% Found x1 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_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found x10:(P z)
% Found (fun (x10:(P z))=> x10) as proof of (P z)
% Found (fun (x10:(P z))=> x10) as proof of (P0 z)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST x00)):(((eq fofType) (cGVB_FIRST x00)) (cGVB_FIRST x00))
% Found (eq_ref0 (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found x04:(((eq fofType) z) (cGVB_FIRST x02))
% Instantiate: a:=z:fofType;b:=(cGVB_FIRST x02):fofType
% Found x04 as proof of (((eq fofType) a) b)
% Found x1:(P z)
% Instantiate: b:=z:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found eq_ref00:=(eq_ref0 (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))):(((eq Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x))))
% Found (eq_ref0 (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) as proof of (((eq Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) b)
% Found ((eq_ref Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) as proof of (((eq Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) b)
% Found ((eq_ref Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) as proof of (((eq Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) b)
% Found ((eq_ref Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN x)))) as proof of (((eq Prop) (((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))->((cGVB_IN z) (cGVB_DOMAIN 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 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found x10:(P z)
% Found (fun (x10:(P z))=> x10) as proof of (P z)
% Found (fun (x10:(P z))=> x10) as proof of (P0 z)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) 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 (cGVB_FIRST x00)):(((eq fofType) (cGVB_FIRST x00)) (cGVB_FIRST x00))
% Found (eq_ref0 (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found x10:(P z)
% Found (fun (x10:(P z))=> x10) as proof of (P z)
% Found (fun (x10:(P z))=> x10) as proof of (P0 z)
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))):(((eq Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt))))))))
% Found (eq_ref0 (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) as proof of (((eq Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) b)
% Found ((eq_ref Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) as proof of (((eq Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) b)
% Found ((eq_ref Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) as proof of (((eq Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) b)
% Found ((eq_ref Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) as proof of (((eq Prop) (((cGVB_IN z) (cGVB_DOMAIN x))->((and (cGVB_M z)) ((ex fofType) (fun (Xt:fofType)=> ((and ((and ((and (cGVB_M Xt)) (cGVB_OPP Xt))) ((cGVB_IN Xt) x))) (((eq fofType) z) (cGVB_FIRST Xt)))))))) b)
% Found x04:(((eq fofType) z) (cGVB_FIRST x02))
% Instantiate: a:=z:fofType;b:=(cGVB_FIRST x02):fofType
% Found x04 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN a)):(((eq fofType) (cGVB_DOMAIN a)) (cGVB_DOMAIN a))
% Found (eq_ref0 (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST x00)):(((eq fofType) (cGVB_FIRST x00)) (cGVB_FIRST x00))
% Found (eq_ref0 (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found x1:(P0 b)
% Instantiate: b:=z:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 z)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 z))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN a)):(((eq fofType) (cGVB_DOMAIN a)) (cGVB_DOMAIN a))
% Found (eq_ref0 (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) 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) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_DOMAIN x))
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% Found conj as proof of b
% Found conj as proof of a
% Found x10:(P z)
% Found (fun (x10:(P z))=> x10) as proof of (P z)
% Found (fun (x10:(P z))=> x10) as proof of (P0 z)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST x00))
% Found x1:(P (cGVB_FIRST x00))
% Instantiate: b:=(cGVB_FIRST x00):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 z):(((eq fofType) z) z)
% Found (eq_ref0 z) as proof of (((eq fofType) z) b0)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b0)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b0)
% Found ((eq_ref fofType) z) as proof of (((eq fofType) z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST x00))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST x00))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN a)):(((eq fofType) (cGVB_DOMAIN a)) (cGVB_DOMAIN a))
% Found (eq_ref0 (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) 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 (cGVB_DOMAIN x)):(((eq fofType) (cGVB_DOMAIN x)) (cGVB_DOMAIN x))
% Found (eq_ref0 (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found ((eq_ref fofType) (cGVB_DOMAIN x)) as proof of (((eq fofType) (cGVB_DOMAIN x)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_DOMAIN a)):(((eq fofType) (cGVB_DOMAIN a)) (cGVB_DOMAIN a))
% Found (eq_ref0 (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) b)
% Found ((eq_ref fofType) (cGVB_DOMAIN a)) as proof of (((eq fofType) (cGVB_DOMAIN a)) 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) x)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) x)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST x00)):(((eq fofType) (cGVB_FIRST x00)) (cGVB_FIRST x00))
% Found (eq_ref0 (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found ((eq_ref fofType) (cGVB_FIRST x00)) as proof of (((eq fofType) (cGVB_FIRST x00)) b)
% Found x1:(P0 b)
% Instantiate: b:=z:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 z)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 z))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x00)
% Found ((eq_ref fofType) a) as
% EOF
%------------------------------------------------------------------------------