TSTP Solution File: SEV338^5 by cocATP---0.2.0

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV338^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n187.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 13:34:04 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV338^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n187.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 08:52:41 CDT 2014
% % CPUTime  : 300.10 
% 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 0x141b830>, <kernel.Constant object at 0x141bc20>) of role type named z
% Using role type
% Declaring z:fofType
% FOF formula (<kernel.Constant object at 0x15f94d0>, <kernel.DependentProduct object at 0x141bcb0>) of role type named cGVB_SECOND
% Using role type
% Declaring cGVB_SECOND:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x141b488>, <kernel.DependentProduct object at 0x141b560>) of role type named cGVB_FIRST
% Using role type
% Declaring cGVB_FIRST:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x141b5a8>, <kernel.DependentProduct object at 0x141b830>) of role type named cGVB_OPP
% Using role type
% Declaring cGVB_OPP:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x141b5f0>, <kernel.DependentProduct object at 0x141b3f8>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x141bcb0>, <kernel.Single object at 0x141b830>) of role type named cGVB_IDENT
% Using role type
% Declaring cGVB_IDENT:fofType
% FOF formula (<kernel.Constant object at 0x141b5a8>, <kernel.DependentProduct object at 0x141b5f0>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula ((iff ((cGVB_IN z) cGVB_IDENT)) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))) of role conjecture named cGVB_AX_IDENT
% Conjecture to prove = ((iff ((cGVB_IN z) cGVB_IDENT)) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))):Prop
% We need to prove ['((iff ((cGVB_IN z) cGVB_IDENT)) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))']
% Parameter fofType:Type.
% Parameter z:fofType.
% Parameter cGVB_SECOND:(fofType->fofType).
% Parameter cGVB_FIRST:(fofType->fofType).
% Parameter cGVB_OPP:(fofType->Prop).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_IDENT:fofType.
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Trying to prove ((iff ((cGVB_IN z) cGVB_IDENT)) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))
% Found eq_ref00:=(eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))):(((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found (eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))):(((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found (eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P0 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P0 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of b
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% 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 x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) 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_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found iff_sym0:=(iff_sym ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))):(forall (B:Prop), (((iff ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))) B)->((iff B) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))))
% Instantiate: b:=(forall (B:Prop), (((iff ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))) B)->((iff B) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))):Prop
% Found iff_sym0 as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% 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 (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))):(((eq Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT)))
% Found (eq_ref0 (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) as proof of (((eq Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) b)
% Found ((eq_ref Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) as proof of (((eq Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) b)
% Found ((eq_ref Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) as proof of (((eq Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) b)
% Found ((eq_ref Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) as proof of (((eq Prop) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: a:=(cGVB_FIRST z):fofType;b:=(cGVB_SECOND z):fofType
% Found x1 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_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))):(((eq Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))
% Found (eq_ref0 (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) as proof of (((eq Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) b)
% Found ((eq_ref Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) as proof of (((eq Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) b)
% Found ((eq_ref Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) as proof of (((eq Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) b)
% Found ((eq_ref Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) as proof of (((eq Prop) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: a:=(cGVB_FIRST z):fofType;b:=(cGVB_SECOND z):fofType
% Found x1 as proof of (((eq fofType) a) b)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found x0 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_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: a:=(cGVB_FIRST z):fofType;b:=(cGVB_SECOND z):fofType
% Found x1 as proof of (((eq fofType) a) b)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found x0 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_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: a:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))):(((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found (eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P0 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% 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 x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: a:=(cGVB_FIRST z):fofType;b:=(cGVB_SECOND z):fofType
% Found x1 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_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: a:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 a)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))):(((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found (eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))):(((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found (eq_ref0 (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found ((eq_ref Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) as proof of (((eq Prop) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P0 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) 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_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% 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_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% 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 x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P2 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 (cGVB_FIRST z))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 (cGVB_FIRST z)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P2 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 (cGVB_FIRST z))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 (cGVB_FIRST z)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b)
% Found x0:(P b)
% Found x0 as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 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) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found x0:(P1 (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P2 b)
% Found x0:(P1 (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% Instantiate: a:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% Found conj as proof of a
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% 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 x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% Found x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: a:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P2 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 (cGVB_FIRST z))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 (cGVB_FIRST z)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P2 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 (cGVB_FIRST z))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 (cGVB_FIRST z)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P (cGVB_FIRST z))
% Found x0 as proof of (P0 (cGVB_FIRST z))
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found x10:(P1 (cGVB_SECOND z))
% Found (fun (x10:(P1 (cGVB_SECOND z)))=> x10) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x10:(P1 (cGVB_SECOND z)))=> x10) as proof of (P2 (cGVB_SECOND z))
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 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_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% 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 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P1 (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P2 b)
% Found x0:(P1 (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of a
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 b)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b0:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: a:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b1)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))->((cGVB_IN z) cGVB_IDENT)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P1 b)
% Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% Found x00:(P1 b)
% Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found x10:(P1 (cGVB_SECOND z))
% Found (fun (x10:(P1 (cGVB_SECOND z)))=> x10) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x10:(P1 (cGVB_SECOND z)))=> x10) as proof of (P2 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% 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 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 b)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 b)
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((cGVB_IN z) cGVB_IDENT)->((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b0:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b0)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b0:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b0)
% Found x0:(P (cGVB_SECOND z))
% Found x0 as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Found x1 as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P0 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x00:(P1 b)
% Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% Found x00:(P1 (cGVB_FIRST z))
% Found (fun (x00:(P1 (cGVB_FIRST z)))=> x00) as proof of (P1 (cGVB_FIRST z))
% Found (fun (x00:(P1 (cGVB_FIRST z)))=> x00) as proof of (P2 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found x0:(P0 (cGVB_FIRST z))
% Found (fun (x0:(P0 (cGVB_FIRST z)))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_FIRST z)))=> x0) as proof of ((P0 (cGVB_FIRST z))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_FIRST z)))=> x0) as proof of (P (cGVB_FIRST z))
% Found x00:(P0 b)
% Found (fun (x00:(P0 b))=> x00) as proof of (P0 b)
% Found (fun (x00:(P0 b))=> x00) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% 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 x0:(P0 b0)
% Instantiate: b0:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: a:=(cGVB_FIRST z):fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 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_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b0:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b0)
% Found x0:(P (cGVB_SECOND z))
% Found x0 as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Found x1 as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P0 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P0 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% 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 x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% Found iff_refl as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found x00:(P0 b)
% Found (fun (x00:(P0 b))=> x00) as proof of (P0 b)
% Found (fun (x00:(P0 b))=> x00) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found x0:(P0 (cGVB_FIRST z))
% Found (fun (x0:(P0 (cGVB_FIRST z)))=> x0) as proof of (P0 (cGVB_FIRST z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_FIRST z)))=> x0) as proof of ((P0 (cGVB_FIRST z))->(P0 (cGVB_FIRST z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_FIRST z)))=> x0) as proof of (P (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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 x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P (cGVB_FIRST z))
% Instantiate: a:=(cGVB_FIRST z):fofType
% Found x0 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) 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 x0:(P0 b0)
% Instantiate: b0:=(cGVB_SECOND z):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (cGVB_SECOND z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (cGVB_SECOND z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b)
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% 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) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% 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_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% 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_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of b
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Found x1 as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_SECOND z))
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% 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) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% 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) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: b:=(cGVB_FIRST z):fofType;b0:=(cGVB_SECOND z):fofType
% Found x1 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_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% 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 x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found x00:(P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P (cGVB_FIRST z))
% Found (fun (x00:(P (cGVB_FIRST z)))=> x00) as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% 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) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% 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) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% 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) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b00)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b00)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b00)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P2 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 (cGVB_FIRST z))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 (cGVB_FIRST z)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P2 b)
% Instantiate: b:=(cGVB_FIRST z):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 (cGVB_FIRST z))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 (cGVB_FIRST z)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: b:=(cGVB_FIRST z):fofType;b0:=(cGVB_SECOND z):fofType
% Found x1 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) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P0 (cGVB_SECOND z))
% Found (fun (x0:(P0 (cGVB_SECOND z)))=> x0) as proof of (P0 (cGVB_SECOND z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_SECOND z)))=> x0) as proof of ((P0 (cGVB_SECOND z))->(P0 (cGVB_SECOND z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_SECOND z)))=> x0) as proof of (P (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% 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 x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% 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) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found x00:(P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P1 (cGVB_SECOND z))
% Found (fun (x00:(P1 (cGVB_SECOND z)))=> x00) as proof of (P2 (cGVB_SECOND z))
% Found x0:(P b)
% Found x0 as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 (cGVB_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found x00:(P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P (cGVB_SECOND z))
% Found (fun (x00:(P (cGVB_SECOND z)))=> x00) as proof of (P0 (cGVB_SECOND z))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 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) 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 x0:(P0 b0)
% Instantiate: b0:=(cGVB_SECOND z):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (cGVB_SECOND z))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (cGVB_SECOND z)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b0)
% Found iff_sym0:=(iff_sym ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))):(forall (B:Prop), (((iff ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))) B)->((iff B) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))))
% Instantiate: b:=(forall (B:Prop), (((iff ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))) B)->((iff B) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))):Prop
% Found iff_sym0 as proof of 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_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b0)
% Found iff_sym0:=(iff_sym ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))):(forall (B:Prop), (((iff ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))) B)->((iff B) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))))))
% Instantiate: b:=(forall (B:Prop), (((iff ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))) B)->((iff B) ((and ((and (cGVB_M z)) (cGVB_OPP z))) (((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z)))))):Prop
% Found iff_sym0 as proof of b
% Found x0:(P (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cGVB_IDENT):(((eq fofType) cGVB_IDENT) cGVB_IDENT)
% Found (eq_ref0 cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b0)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b0)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b0)
% Found ((eq_ref fofType) cGVB_IDENT) as proof of (((eq fofType) cGVB_IDENT) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P1 (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P2 b)
% Found x0:(P1 (cGVB_SECOND z))
% Instantiate: b:=(cGVB_SECOND z):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% 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_FIRST z)):(((eq fofType) (cGVB_FIRST z)) (cGVB_FIRST z))
% Found (eq_ref0 (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found ((eq_ref fofType) (cGVB_FIRST z)) as proof of (((eq fofType) (cGVB_FIRST z)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cGVB_IDENT)
% 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_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: a:=(cGVB_FIRST z):fofType;b:=(cGVB_SECOND z):fofType
% Found x1 as proof of (((eq fofType) a) b)
% Found x0:(P b)
% Found x0 as proof of (P0 (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_FIRST z))
% Found eq_ref00:=(eq_ref0 (cGVB_SECOND z)):(((eq fofType) (cGVB_SECOND z)) (cGVB_SECOND z))
% Found (eq_ref0 (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found ((eq_ref fofType) (cGVB_SECOND z)) as proof of (((eq fofType) (cGVB_SECOND z)) b1)
% Found x1:(((eq fofType) (cGVB_FIRST z)) (cGVB_SECOND z))
% Instantiate: 
% EOF
%------------------------------------------------------------------------------