TSTP Solution File: SEV360^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV360^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n183.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 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV360^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n183.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 08:56:41 CDT 2014
% % CPUTime : 300.03
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x25f3878>, <kernel.Constant object at 0x25f3c68>) of role type named z
% Using role type
% Declaring z:fofType
% FOF formula (<kernel.Constant object at 0x24d4fc8>, <kernel.Single object at 0x25f3ab8>) of role type named y
% Using role type
% Declaring y:fofType
% FOF formula (<kernel.Constant object at 0x25f3950>, <kernel.Single object at 0x25f36c8>) of role type named f
% Using role type
% Declaring f:fofType
% FOF formula (<kernel.Constant object at 0x25f3878>, <kernel.DependentProduct object at 0x25f3638>) of role type named cGVB_SECOND
% Using role type
% Declaring cGVB_SECOND:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x25f3a28>, <kernel.DependentProduct object at 0x25f3950>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x25f3cf8>, <kernel.DependentProduct object at 0x25f3680>) of role type named cGVB_FIRST
% Using role type
% Declaring cGVB_FIRST:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x25f36c8>, <kernel.DependentProduct object at 0x25f3878>) of role type named cGVB_OPP
% Using role type
% Declaring cGVB_OPP:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x25f3830>, <kernel.DependentProduct object at 0x25f35f0>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x25f3950>, <kernel.DependentProduct object at 0x25f36c8>) of role type named cGVB_APPLY
% Using role type
% Declaring cGVB_APPLY:(fofType->(fofType->fofType))
% FOF formula ((iff ((cGVB_IN z) ((cGVB_APPLY f) y))) ((and (cGVB_M z)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))) of role conjecture named cGVB_AX_APPLY
% Conjecture to prove = ((iff ((cGVB_IN z) ((cGVB_APPLY f) y))) ((and (cGVB_M z)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))):Prop
% We need to prove ['((iff ((cGVB_IN z) ((cGVB_APPLY f) y))) ((and (cGVB_M z)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))))']
% Parameter fofType:Type.
% Parameter z:fofType.
% Parameter y:fofType.
% Parameter f:fofType.
% Parameter cGVB_SECOND:(fofType->fofType).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_FIRST:(fofType->fofType).
% Parameter cGVB_OPP:(fofType->Prop).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_APPLY:(fofType->(fofType->fofType)).
% Trying to prove ((iff ((cGVB_IN z) ((cGVB_APPLY f) y))) ((and (cGVB_M z)) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))):(((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found (eq_ref0 ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% 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 (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))):(((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found (eq_ref0 ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) as proof of (((eq Prop) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% 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 (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))):(((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (eq_ref0 (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))):(((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found (eq_ref0 (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) as proof of (((eq (fofType->Prop)) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((and ((and ((and ((and (cGVB_M x)) (cGVB_OPP x))) ((cGVB_IN x) f))) (((eq fofType) (cGVB_FIRST x)) y))) ((cGVB_IN z) (cGVB_SECOND x)))))
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((and ((and ((and ((and (cGVB_M x)) (cGVB_OPP x))) ((cGVB_IN x) f))) (((eq fofType) (cGVB_FIRST x)) y))) ((cGVB_IN z) (cGVB_SECOND x)))))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 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) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((and ((and ((and ((and (cGVB_M x)) (cGVB_OPP x))) ((cGVB_IN x) f))) (((eq fofType) (cGVB_FIRST x)) y))) ((cGVB_IN z) (cGVB_SECOND x)))))
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) ((and ((and ((and ((and (cGVB_M x0)) (cGVB_OPP x0))) ((cGVB_IN x0) f))) (((eq fofType) (cGVB_FIRST x0)) y))) ((cGVB_IN z) (cGVB_SECOND x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((and ((and ((and ((and (cGVB_M x)) (cGVB_OPP x))) ((cGVB_IN x) f))) (((eq fofType) (cGVB_FIRST x)) y))) ((cGVB_IN z) (cGVB_SECOND x)))))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P 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 (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% 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 eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (P (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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 (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw))))))
% 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_ref000:=(eq_ref00 P0):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found ((eq_ref0 ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found ((eq_ref0 ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))):(((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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 x7:(((eq fofType) (cGVB_FIRST x2)) y)
% Instantiate: a:=(cGVB_FIRST x2):fofType
% Found x7 as proof of (((eq fofType) a) y)
% Found x7:(((eq fofType) (cGVB_FIRST x2)) y)
% Instantiate: a:=(cGVB_FIRST x2):fofType
% Found x7 as proof of (((eq fofType) a) y)
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found ((eq_ref0 ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found ((eq_ref0 ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found (((eq_ref fofType) ((cGVB_APPLY f) y)) P0) as proof of (P1 ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 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) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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 x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))):(((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% 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 x7:(((eq fofType) (cGVB_FIRST x2)) y)
% Instantiate: a:=(cGVB_FIRST x2):fofType
% Found x7 as proof of (((eq fofType) a) y)
% Found x7:(((eq fofType) (cGVB_FIRST x2)) y)
% Instantiate: a:=(cGVB_FIRST x2):fofType
% Found x7 as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found x60:=(x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found x60:=(x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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) (cGVB_FIRST x2))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cGVB_FIRST x2))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cGVB_FIRST x2))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cGVB_FIRST x2))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cGVB_FIRST x2))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cGVB_FIRST x2))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cGVB_FIRST x2))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cGVB_FIRST x2))
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of ((cGVB_IN z) b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))))) as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of ((cGVB_IN z) b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of ((cGVB_IN z) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of ((cGVB_IN z) b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of ((cGVB_IN z) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))):(((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))):(((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))):(((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found x5 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) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x2))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xw:fofType)=> ((and ((and ((and ((and (cGVB_M Xw)) (cGVB_OPP Xw))) ((cGVB_IN Xw) f))) (((eq fofType) (cGVB_FIRST Xw)) y))) ((cGVB_IN z) (cGVB_SECOND Xw)))))
% 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_APPLY f) (cGVB_FIRST x2))):(((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) as proof of (((eq fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY f) y)):(((eq fofType) ((cGVB_APPLY f) y)) ((cGVB_APPLY f) y))
% Found (eq_ref0 ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY f) y)) as proof of (((eq fofType) ((cGVB_APPLY f) y)) b)
% Found x7:(((eq fofType) (cGVB_FIRST x2)) y)
% Instantiate: a:=(cGVB_FIRST x2):fofType
% Found x7 as proof of (((eq fofType) a) y)
% Found x7:(((eq fofType) (cGVB_FIRST x2)) y)
% Instantiate: a:=(cGVB_FIRST x2):fofType
% Found x7 as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN z) (cGVB_SECOND x0))):(((eq Prop) ((cGVB_IN z) (cGVB_SECOND x0))) ((cGVB_IN z) (cGVB_SECOND x0)))
% Found (eq_ref0 ((cGVB_IN z) (cGVB_SECOND x0))) as proof of (((eq Prop) ((cGVB_IN z) (cGVB_SECOND x0))) b)
% Found ((eq_ref Prop) ((cGVB_IN z) (cGVB_SECOND x0))) as proof of (((eq Prop) ((cGVB_IN z) (cGVB_SECOND x0))) b)
% Found ((eq_ref Prop) ((cGVB_IN z) (cGVB_SECOND x0))) as proof of (((eq Prop) ((cGVB_IN z) (cGVB_SECOND x0))) b)
% Found ((eq_ref Prop) ((cGVB_IN z) (cGVB_SECOND x0))) as proof of (((eq Prop) ((cGVB_IN z) (cGVB_SECOND x0))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x2)):(((eq fofType) (cGVB_SECOND x2)) (cGVB_SECOND x2))
% Found (eq_ref0 (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x2)) as proof of (((eq fofType) (cGVB_SECOND x2)) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: a:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P a)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P a)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: a:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P a)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P a)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P a)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: a:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P a)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P a)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P a)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P a)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of (P a)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: a:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P a)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P a)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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 x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: a:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (P a)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->(P a))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->(P a)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of (P a)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) (P a)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P a)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: a:=(cGVB_SECOND x2):fofType
% Found x5 as proof of (P a)
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_APPLY f) (cGVB_FIRST x2)))->(P0 ((cGVB_APPLY f) (cGVB_FIRST x2))))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found ((eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_APPLY f) (cGVB_FIRST x2)))->(P0 ((cGVB_APPLY f) (cGVB_FIRST x2))))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found ((eq_ref0 ((cGVB_APPLY f) (cGVB_FIRST x2))) P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found (((eq_ref fofType) ((cGVB_APPLY f) (cGVB_FIRST x2))) P0) as proof of (P1 ((cGVB_APPLY f) (cGVB_FIRST x2)))
% Found x60:=(x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found x60:=(x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))):((P0 ((cGVB_APPLY f) y))->(P0 ((cGVB_APPLY f) y)))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found (x6 (fun (x7:fofType)=> (P0 ((cGVB_APPLY f) y)))) as proof of (P1 ((cGVB_APPLY f) y))
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of ((cGVB_IN z) b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) (cGVB_SECOND x2)))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found ((eq_ref0 (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y)))=> (((eq_ref fofType) (cGVB_SECOND x2)) (cGVB_IN z))))) as proof of ((cGVB_IN z) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of ((cGVB_IN z) b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of (P b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of ((cGVB_IN z) b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of ((cGVB_IN z) b)
% Found x5:((cGVB_IN z) (cGVB_SECOND x2))
% Instantiate: b:=(cGVB_SECOND x2):fofType
% Found (fun (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of ((cGVB_IN z) b)
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b))
% Found (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5) as proof of (((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5)) as proof of ((cGVB_IN z) b)
% Found (fun (x3:((and ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))))=> (((fun (P0:Type) (x4:(((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))->(((cGVB_IN z) (cGVB_SECOND x2))->P0)))=> (((((and_rect ((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) ((cGVB_IN z) (cGVB_SECOND x2))) P0) x4) x3)) ((cGVB_IN z) b)) (fun (x4:((and ((and ((and (cGVB_M x2)) (cGVB_OPP x2))) ((cGVB_IN x2) f))) (((eq fofType) (cGVB_FIRST x2)) y))) (x5:((cGVB_IN z) (cGVB_SECOND x2)))=> x5))) as proof of ((cGVB_IN z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY f) y))
% 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) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a)
% EOF
%------------------------------------------------------------------------------