TSTP Solution File: SEV377^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV377^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n105.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 13:34:07 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV377^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n105.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 08:59:56 CDT 2014
% % CPUTime  : 300.09 
% 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 0x1f7d7e8>, <kernel.DependentProduct object at 0x1f7dfc8>) of role type named cGVB_COMPOSE
% Using role type
% Declaring cGVB_COMPOSE:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x218a128>, <kernel.DependentProduct object at 0x1f7dfc8>) of role type named cGVB_APPLY
% Using role type
% Declaring cGVB_APPLY:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1f7dea8>, <kernel.DependentProduct object at 0x1f7dd40>) of role type named cGVB_DOMAIN
% Using role type
% Declaring cGVB_DOMAIN:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1f7da28>, <kernel.DependentProduct object at 0x1f7dcb0>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f7d638>, <kernel.DependentProduct object at 0x1f7d5f0>) of role type named cGVB_FUNCTION
% Using role type
% Declaring cGVB_FUNCTION:(fofType->Prop)
% FOF formula (forall (Xf:fofType) (Xg:fofType) (Xx:fofType), (((and (cGVB_FUNCTION Xf)) ((cGVB_IN Xx) (cGVB_DOMAIN Xf)))->(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))) of role conjecture named cGVB_APP_PROP_1
% Conjecture to prove = (forall (Xf:fofType) (Xg:fofType) (Xx:fofType), (((and (cGVB_FUNCTION Xf)) ((cGVB_IN Xx) (cGVB_DOMAIN Xf)))->(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xf:fofType) (Xg:fofType) (Xx:fofType), (((and (cGVB_FUNCTION Xf)) ((cGVB_IN Xx) (cGVB_DOMAIN Xf)))->(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))))']
% Parameter fofType:Type.
% Parameter cGVB_COMPOSE:(fofType->(fofType->fofType)).
% Parameter cGVB_APPLY:(fofType->(fofType->fofType)).
% Parameter cGVB_DOMAIN:(fofType->fofType).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_FUNCTION:(fofType->Prop).
% Trying to prove (forall (Xf:fofType) (Xg:fofType) (Xx:fofType), (((and (cGVB_FUNCTION Xf)) ((cGVB_IN Xx) (cGVB_DOMAIN Xf)))->(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))))
% Found x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x0:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x0:(P0 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P0 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P0 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P 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 x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found x0:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found x2:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x0:(P0 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x00:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x00) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x0:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: a:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):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) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P0 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% Found x0:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x0:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P0 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x2:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: a:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found x2 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x20:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x20) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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 x10:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x10:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x10) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x10:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x10) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: a:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P0 a)
% Found x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P2 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P2 b))=> x2) as proof of (P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of ((P2 b)->(P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P2 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P2 b))=> x2) as proof of (P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of ((P2 b)->(P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x2:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x2:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P2 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P2 b))=> x2) as proof of (P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of ((P2 b)->(P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P2 b)
% Instantiate: b:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P2 b))=> x2) as proof of (P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of ((P2 b)->(P2 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P2:(fofType->Prop)) (x2:(P2 b))=> x2) as proof of (P1 b)
% Found x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% Found x2:(P b)
% Found x2 as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% 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 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):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 x2:(P b)
% Instantiate: b0:=b:fofType
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x2:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x2:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x30:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x30:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x30) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x30:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x30) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b0:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):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 eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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 x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: a:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x2:(P b)
% Found x2 as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x2:(P b)
% Instantiate: b0:=b:fofType
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x0:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x0) as proof of ((P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x0) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: a:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x30:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x30:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x30) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x30:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x30) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% 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_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x20:(P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P2 b)
% Found x20:(P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P2 b)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x2:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b0))=> x2) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x0:(P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b0:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 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 eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x2:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b0))=> x2) as proof of (P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% Found x2:(P b)
% Instantiate: b0:=b:fofType
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 x20:(P b0)
% Found (fun (x20:(P b0))=> x20) as proof of (P b0)
% Found (fun (x20:(P b0))=> x20) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x0) as proof of ((P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x0) as proof of (P b0)
% Found x20:(P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P2 b)
% Found x20:(P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P1 b)
% Found (fun (x20:(P1 b))=> x20) as proof of (P2 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_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x2:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b0))=> x2) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x2:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b0))=> x2) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x2:(P b)
% Found x2 as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x0:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x0:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b)
% Found x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x00:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x00) as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b0:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 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 eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b1)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% 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 eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Instantiate: b0:=((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx):fofType
% Found x2 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 eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found x2:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (fun (x2:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x2) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x2:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x2) as proof of ((P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))))=> x2) as proof of (P ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_APPLY Xf) Xx))
% Found x2:(P ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found x2 as proof of (P0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) 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 x20:(P b0)
% Found (fun (x20:(P b0))=> x20) as proof of (P b0)
% Found (fun (x20:(P b0))=> x20) as proof of (P0 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_APPLY Xg) ((cGVB_APPLY Xf) Xx))):(((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found (eq_ref0 ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) as proof of (((eq fofType) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% 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 x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (fun (x20:(P1 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)))=> x20) as proof of (P2 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)):(((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx))
% Found (eq_ref0 ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found ((eq_ref fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) as proof of (((eq fofType) ((cGVB_APPLY ((cGVB_COMPOSE Xg) Xf)) Xx)) b0)
% Found x2:(P0 b0)
% Instantiate: b0:=((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)):fofType
% Found (fun (x2:(P0 b0))=> x2) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_APPLY Xg) ((cGVB_APPLY Xf) Xx)))
% Found ((eq_ref fofType)
% EOF
%------------------------------------------------------------------------------