TSTP Solution File: SEV331^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV331^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n179.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 13:34:03 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV331^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 08:51:51 CDT 2014
% % CPUTime : 300.02
% 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 0x1da7ef0>, <kernel.Constant object at 0x1da7f80>) of role type named y
% Using role type
% Declaring y:fofType
% FOF formula (<kernel.Constant object at 0x1da5c68>, <kernel.Single object at 0x1da7368>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0x1da7200>, <kernel.DependentProduct object at 0x1da7ef0>) of role type named cGVB_NOP
% Using role type
% Declaring cGVB_NOP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1da72d8>, <kernel.DependentProduct object at 0x1da75f0>) of role type named cGVB_SING
% Using role type
% Declaring cGVB_SING:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1da7d40>, <kernel.DependentProduct object at 0x1da7200>) of role type named cGVB_OP
% Using role type
% Declaring cGVB_OP:(fofType->(fofType->fofType))
% FOF formula (((eq fofType) ((cGVB_OP x) y)) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) of role conjecture named cGVB_AX_OP
% Conjecture to prove = (((eq fofType) ((cGVB_OP x) y)) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):Prop
% We need to prove ['(((eq fofType) ((cGVB_OP x) y)) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))']
% Parameter fofType:Type.
% Parameter y:fofType.
% Parameter x:fofType.
% Parameter cGVB_NOP:(fofType->(fofType->fofType)).
% Parameter cGVB_SING:(fofType->fofType).
% Parameter cGVB_OP:(fofType->(fofType->fofType)).
% Trying to prove (((eq fofType) ((cGVB_OP x) y)) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P ((cGVB_OP x) y))
% Found (fun (x01:(P ((cGVB_OP x) y)))=> x01) as proof of (P ((cGVB_OP x) y))
% Found (fun (x01:(P ((cGVB_OP x) y)))=> x01) as proof of (P0 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P ((cGVB_OP x) y))
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P0 b)
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((cGVB_OP x) y))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((cGVB_OP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found x02:(P ((cGVB_OP x) y))
% Found (fun (x02:(P ((cGVB_OP x) y)))=> x02) as proof of (P ((cGVB_OP x) y))
% Found (fun (x02:(P ((cGVB_OP x) y)))=> x02) as proof of (P0 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found x01:(P ((cGVB_OP x) y))
% Found (fun (x01:(P ((cGVB_OP x) y)))=> x01) as proof of (P ((cGVB_OP x) y))
% Found (fun (x01:(P ((cGVB_OP x) y)))=> x01) as proof of (P0 ((cGVB_OP x) y))
% Found x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P ((cGVB_OP x) y))
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P0 b)
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((cGVB_OP x) y))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((cGVB_OP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found x02:(P ((cGVB_OP x) y))
% Found (fun (x02:(P ((cGVB_OP x) y)))=> x02) as proof of (P ((cGVB_OP x) y))
% Found (fun (x02:(P ((cGVB_OP x) y)))=> x02) as proof of (P0 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P ((cGVB_OP x) y))
% Instantiate: a:=((cGVB_OP x) y):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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_OP x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_OP x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_OP x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_OP x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: a:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):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_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_OP x) y):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 x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):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 x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x01:(P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0 as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x0:(P0 ((cGVB_OP x) y))
% Found (fun (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of ((P0 ((cGVB_OP x) y))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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 x01:(P0 b)
% Found (fun (x01:(P0 b))=> x01) as proof of (P0 b)
% Found (fun (x01:(P0 b))=> x01) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P0 b0)
% Found x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of ((P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))->(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x00:(P 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 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x02:(P b)
% Found (fun (x02:(P b))=> x02) as proof of (P b)
% Found (fun (x02:(P b))=> x02) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x0:(P ((cGVB_OP x) y))
% Instantiate: a:=((cGVB_OP x) y):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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_OP x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_OP x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_OP x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_OP x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: a:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):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_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: a:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):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_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_OP x) y):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 x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):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 x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x01:(P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P0 b0)
% Found x01:(P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0 as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 ((cGVB_OP x) y))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 ((cGVB_OP x) y)))
% 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_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0 as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x0:(P0 ((cGVB_OP x) y))
% Found (fun (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of ((P0 ((cGVB_OP x) y))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P ((cGVB_OP x) y))
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x0:(P0 ((cGVB_OP x) y))
% Found (fun (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of ((P0 ((cGVB_OP x) y))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x01:(P0 b)
% Found (fun (x01:(P0 b))=> x01) as proof of (P0 b)
% Found (fun (x01:(P0 b))=> x01) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b0)
% Found x01:(P0 b)
% Found (fun (x01:(P0 b))=> x01) as proof of (P0 b)
% Found (fun (x01:(P0 b))=> x01) as proof of (P1 b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P0 b0)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):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 x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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 x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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 x0:(P ((cGVB_OP x) y))
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 ((cGVB_OP x) y))
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of ((P0 ((cGVB_OP x) y))->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_OP x) y)))=> x0) as proof of (P b0)
% Found x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of ((P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))->(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of ((P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x00:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x00 as proof of (P2 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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 x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x01:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x01) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x01:(P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x02:(P b)
% Found (fun (x02:(P b))=> x02) as proof of (P b)
% Found (fun (x02:(P b))=> x02) 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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 x02:(P ((cGVB_OP x) y))
% Found (fun (x02:(P ((cGVB_OP x) y)))=> x02) as proof of (P ((cGVB_OP x) y))
% Found (fun (x02:(P ((cGVB_OP x) y)))=> x02) as proof of (P0 ((cGVB_OP x) y))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found x0:(P1 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P1 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x01:(P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P b0)
% Found (fun (x01:(P b0))=> x01) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b00)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b00)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b00)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b00)
% Found x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x02:(P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x02) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x00:(P1 b)
% Instantiate: b0:=b:fofType
% Found x00 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P1 b)
% Found x0 as proof of (P2 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P1 b)
% Found x0 as proof of (P2 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: a:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 a)
% Found x0:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Instantiate: a:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found x0 as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) 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 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x1:(P2 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x00:(P2 b0)
% Instantiate: b0:=((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)):fofType
% Found (fun (x00:(P2 b0))=> x00) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b0))=> x00) as proof of ((P2 b0)->(P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b0))=> x00) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found x10:(P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of ((P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))->(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x0) as proof of (P ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found x0:(P b)
% Instantiate: a:=b:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b1)
% Found x00:(P1 ((cGVB_OP x) y))
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found x00 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 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 x0:(P b0)
% Found x0 as proof of (P0 ((cGVB_OP x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_OP x) y)):(((eq fofType) ((cGVB_OP x) y)) ((cGVB_OP x) y))
% Found (eq_ref0 ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_OP x) y)) as proof of (((eq fofType) ((cGVB_OP x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x00:(P2 ((cGVB_OP x) y))
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x00:(P2 ((cGVB_OP x) y)))=> x00) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 ((cGVB_OP x) y)))=> x00) as proof of ((P2 ((cGVB_OP x) y))->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 ((cGVB_OP x) y)))=> x00) as proof of (P1 b0)
% Found x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (fun (x000:(P1 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))))=> x000) as proof of (P2 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% 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_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))):(((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y)))
% Found (eq_ref0 ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found ((eq_ref fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) as proof of (((eq fofType) ((cGVB_NOP (cGVB_SING x)) ((cGVB_NOP x) y))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_OP x) y):fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (
% EOF
%------------------------------------------------------------------------------