TSTP Solution File: SEV365^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV365^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n090.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 13:34:06 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV365^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n090.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 08:57:56 CDT 2014
% % CPUTime : 300.03
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1a9f5f0>, <kernel.Constant object at 0x1a9f878>) of role type named h
% Using role type
% Declaring h:fofType
% FOF formula (<kernel.Constant object at 0x1b2c3b0>, <kernel.Single object at 0x1a9f518>) of role type named f2
% Using role type
% Declaring f2:fofType
% FOF formula (<kernel.Constant object at 0x1a9f128>, <kernel.Single object at 0x1a9f200>) of role type named f1
% Using role type
% Declaring f1:fofType
% FOF formula (<kernel.Constant object at 0x1a9f5f0>, <kernel.Single object at 0x1a9f4d0>) of role type named s1
% Using role type
% Declaring s1:fofType
% FOF formula (<kernel.Constant object at 0x1a9f0e0>, <kernel.Single object at 0x1a9f638>) of role type named s2
% Using role type
% Declaring s2:fofType
% FOF formula (<kernel.Constant object at 0x1a9f128>, <kernel.DependentProduct object at 0x1a9f908>) of role type named cGVB_APPLY
% Using role type
% Declaring cGVB_APPLY:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1532ab8>, <kernel.DependentProduct object at 0x1a9f908>) of role type named cGVB_APP2
% Using role type
% Declaring cGVB_APP2:(fofType->(fofType->(fofType->fofType)))
% FOF formula (<kernel.Constant object at 0x1a9f3b0>, <kernel.DependentProduct object at 0x1a9f248>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1a9f5f0>, <kernel.DependentProduct object at 0x1a9f248>) of role type named cGVB_MAPS
% Using role type
% Declaring cGVB_MAPS:(fofType->(fofType->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1a9f830>, <kernel.DependentProduct object at 0x1621ef0>) of role type named cGVB_CLOSED
% Using role type
% Declaring cGVB_CLOSED:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1a9f998>, <kernel.DependentProduct object at 0x1621950>) of role type named cGVB_HOMOM
% Using role type
% Declaring cGVB_HOMOM:(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% FOF formula ((iff (((((cGVB_HOMOM h) s1) f1) s2) f2)) ((and ((and ((and ((cGVB_CLOSED s1) f1)) ((cGVB_CLOSED s2) f2))) (((cGVB_MAPS h) s1) s2))) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))) of role conjecture named cGVB_AX_HOMOM
% Conjecture to prove = ((iff (((((cGVB_HOMOM h) s1) f1) s2) f2)) ((and ((and ((and ((cGVB_CLOSED s1) f1)) ((cGVB_CLOSED s2) f2))) (((cGVB_MAPS h) s1) s2))) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))):Prop
% We need to prove ['((iff (((((cGVB_HOMOM h) s1) f1) s2) f2)) ((and ((and ((and ((cGVB_CLOSED s1) f1)) ((cGVB_CLOSED s2) f2))) (((cGVB_MAPS h) s1) s2))) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))))']
% Parameter fofType:Type.
% Parameter h:fofType.
% Parameter f2:fofType.
% Parameter f1:fofType.
% Parameter s1:fofType.
% Parameter s2:fofType.
% Parameter cGVB_APPLY:(fofType->(fofType->fofType)).
% Parameter cGVB_APP2:(fofType->(fofType->(fofType->fofType))).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_MAPS:(fofType->(fofType->(fofType->Prop))).
% Parameter cGVB_CLOSED:(fofType->(fofType->Prop)).
% Parameter cGVB_HOMOM:(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))).
% Trying to prove ((iff (((((cGVB_HOMOM h) s1) f1) s2) f2)) ((and ((and ((and ((cGVB_CLOSED s1) f1)) ((cGVB_CLOSED s2) f2))) (((cGVB_MAPS h) s1) s2))) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))):(((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found (eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))):(((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found (eq_ref0 (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) as proof of (((eq Prop) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))))) b)
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found x1:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x1:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found eq_ref00:=(eq_ref0 f2):(((eq fofType) f2) f2)
% Found (eq_ref0 f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found ((eq_ref fofType) f2) as proof of (((eq fofType) f2) b)
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType) (Xy:fofType), (((and ((cGVB_IN Xx) s1)) ((cGVB_IN Xy) s1))->(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))))
% Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% Instantiate: b:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% Found eq_sym0 as proof of b
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found x3:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% 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 x3:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found x1:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found x3:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found x1:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found x1:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: a:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x1 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% 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 x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% 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_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found x1:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: a:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x1 as proof of (P0 a)
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x10:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x10) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% 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_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% 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 x3:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P2 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P2 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% Found x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P b)
% Found x1 as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: a:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of a
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found x1:(P1 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P2 b)
% Found x1:(P1 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY h) Xy))
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) f2)
% 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_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found x3:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x3 as proof of (P0 b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: a:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 a)
% Found x3:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Instantiate: a:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found x3 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: a:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of a
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P2 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x1:(P2 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% Found x1:(P b)
% Found x1 as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x10:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x10) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x30:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x30) as proof of (P0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (x30:(P ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))=> x30) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))):(((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (eq_ref0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) as proof of (((eq fofType) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found x20:(P1 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x20:(P1 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x20) as proof of (P1 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (fun (x20:(P1 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))))=> x20) as proof of (P2 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found x1:(P (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Instantiate: b:=(((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((cGVB_APP2 f1) Xx) Xy))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% 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 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))):(((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found (eq_ref0 (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found ((eq_ref fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) as proof of (((eq fofType) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy))) b)
% Found x3:(P0 b)
% Instantiate: b:=((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)):fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy)))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 ((cGVB_APPLY h) (((cGVB_APP2 f1) Xx) Xy))))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((cGVB_APP2 f2) ((cGVB_APPLY h) Xx)) ((cGVB_APPLY h) Xy)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((cGVB_APP2 f2
% EOF
%------------------------------------------------------------------------------