TSTP Solution File: SEV355^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV355^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n186.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 300.06s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV355^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n186.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:55:26 CDT 2014
% % CPUTime : 300.06
% 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 0x1e88dd0>, <kernel.Constant object at 0x1e88710>) of role type named z
% Using role type
% Declaring z:fofType
% FOF formula (<kernel.Constant object at 0x23a15f0>, <kernel.Single object at 0x1e88320>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0x23a15f0>, <kernel.DependentProduct object at 0x1fc4c68>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e88fc8>, <kernel.DependentProduct object at 0x1fc4950>) of role type named cGVB_OP
% Using role type
% Declaring cGVB_OP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1e88878>, <kernel.DependentProduct object at 0x1fc4e60>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1e88fc8>, <kernel.DependentProduct object at 0x1fc48c0>) of role type named cGVB_SECOND
% Using role type
% Declaring cGVB_SECOND:(fofType->fofType)
% FOF formula ((iff ((cGVB_IN z) (cGVB_SECOND x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))) of role conjecture named cGVB_AX_SECOND
% Conjecture to prove = ((iff ((cGVB_IN z) (cGVB_SECOND x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))):Prop
% We need to prove ['((iff ((cGVB_IN z) (cGVB_SECOND x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))))']
% Parameter fofType:Type.
% Parameter z:fofType.
% Parameter x:fofType.
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_OP:(fofType->(fofType->fofType)).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_SECOND:(fofType->fofType).
% Trying to prove ((iff ((cGVB_IN z) (cGVB_SECOND x))) ((and (cGVB_M z)) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))):(((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found (eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) 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 (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))):(((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found (eq_ref0 ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found ((eq_ref Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) as proof of (((eq Prop) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% 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 (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P x03)
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found eq_ref00:=(eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found (eq_ref0 (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x0)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x0) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x0)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x0) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P x03)
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x0)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x0) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x0)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x0) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found x0:((cGVB_IN z) (cGVB_SECOND x))
% Instantiate: x01:=(cGVB_SECOND x):fofType
% Found x0 as proof of ((cGVB_IN z) x01)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% 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 iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% Found iff_refl as proof of b
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found x0:((cGVB_IN z) (cGVB_SECOND x))
% Instantiate: x01:=(cGVB_SECOND x):fofType
% Found x0 as proof of ((cGVB_IN z) x01)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found x05 as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv)))))))
% 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_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P x03)
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found x05 as proof of (P b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found x05 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P x03)
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P x03)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found x05 as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP Xu) Xv)))) ((cGVB_IN z) Xv))))))
% 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_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))):(((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv))))
% Found (eq_ref0 (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found x05 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))):(((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv))))
% Found (eq_ref0 (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) as proof of (((eq (fofType->Prop)) (fun (Xv:fofType)=> ((and ((and ((and (cGVB_M x00)) (cGVB_M Xv))) (((eq fofType) x) ((cGVB_OP x00) Xv)))) ((cGVB_IN z) Xv)))) b)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))) ((cGVB_IN z) x0))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))) ((cGVB_IN z) x0))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of ((cGVB_IN z) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: a:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of a
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: a:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of a
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found x05 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))) ((cGVB_IN z) x0))))
% Found eq_ref00:=(eq_ref0 (f x01)):(((eq Prop) (f x01)) (f x01))
% Found (eq_ref0 (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found ((eq_ref Prop) (f x01)) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (((eq Prop) (f x01)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x01))) (((eq fofType) x) ((cGVB_OP x00) x01)))) ((cGVB_IN z) x01)))
% Found (fun (x01:fofType)=> ((eq_ref Prop) (f x01))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and ((and (cGVB_M x00)) (cGVB_M x0))) (((eq fofType) x) ((cGVB_OP x00) x0)))) ((cGVB_IN z) x0))))
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P a)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P a)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) 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_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found x05 as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of ((cGVB_IN z) b)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of ((cGVB_IN z) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of ((cGVB_IN z) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of ((cGVB_IN z) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: b:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of ((cGVB_IN z) b)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->((cGVB_IN z) b))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->((cGVB_IN z) b)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found ((and_rect1 ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of ((cGVB_IN z) b)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) ((cGVB_IN z) b)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) 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_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) 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 x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 x03):(((eq fofType) x03) x03)
% Found (eq_ref0 x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found ((eq_ref fofType) x03) as proof of (((eq fofType) x03) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref000:=(eq_ref00 P0):((P0 (cGVB_SECOND x))->(P0 (cGVB_SECOND x)))
% Found (eq_ref00 P0) as proof of (P1 (cGVB_SECOND x))
% Found ((eq_ref0 (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found (((eq_ref fofType) (cGVB_SECOND x)) P0) as proof of (P1 (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P a)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) as proof of (P a)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z)))) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03))))=> (((eq_ref fofType) x03) (cGVB_IN z))))) 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) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x03)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found (fun (x05:((cGVB_IN z) x03))=> x05) as proof of (P a)
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((cGVB_IN z) x03)->(P a))
% Found (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05) as proof of (((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->(P a)))
% Found (and_rect10 (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found ((and_rect1 (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05)) as proof of (P a)
% Found (fun (x10:((and ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)))=> (((fun (P0:Type) (x2:(((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))->(((cGVB_IN z) x03)->P0)))=> (((((and_rect ((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) ((cGVB_IN z) x03)) P0) x2) x10)) (P a)) (fun (x04:((and ((and (cGVB_M x02)) (cGVB_M x03))) (((eq fofType) x) ((cGVB_OP x02) x03)))) (x05:((cGVB_IN z) x03))=> x05))) as proof of (P a)
% Found x05:((cGVB_IN z) x03)
% Instantiate: a:=x03:fofType
% Found x05 as proof of (P a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND x)):(((eq fofType) (cGVB_SECOND x)) (cGVB_SECOND x))
% Found (eq_ref0 (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found ((eq_ref fofType) (cGVB_SECOND x)) as proof of (((eq fofType) (cGVB_SECOND x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND x))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) 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_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P0 x03)
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (P0 x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P0 x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P0 x03)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P0 x03)
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (P0 x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P0 x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P0 x03)
% Found eq_ref000:=(eq_ref00 (cGVB_IN z)):(((cGVB_IN z) x03)->((cGVB_IN z) x03))
% Found (eq_ref00 (cGVB_IN z)) as proof of (P0 x03)
% Found ((eq_ref0 x03) (cGVB_IN z)) as proof of (P0 x03)
% Found (((eq_ref fofType) x03) (cGVB_IN z)) as proof of (P0 x03)
% Found (((eq_ref fofType) x0
% EOF
%------------------------------------------------------------------------------