%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV330^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.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 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV330^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.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 08:51:46 CDT 2014
% % CPUTime  : 300.03 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0xae57e8>, <kernel.Constant object at 0xae5908>) of role type named y
% Using role type
% Declaring y:fofType
% FOF formula (<kernel.Constant object at 0xd3a488>, <kernel.Single object at 0xae5638>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0xae5c68>, <kernel.DependentProduct object at 0xae4c20>) of role type named cGVB_COMPLEMENT
% Using role type
% Declaring cGVB_COMPLEMENT:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xae5878>, <kernel.DependentProduct object at 0xae4320>) of role type named cGVB_INTERSECT
% Using role type
% Declaring cGVB_INTERSECT:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xae57e8>, <kernel.DependentProduct object at 0xae45f0>) of role type named cGVB_UNION
% Using role type
% Declaring cGVB_UNION:(fofType->(fofType->fofType))
% FOF formula (((eq fofType) ((cGVB_UNION x) y)) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) of role conjecture named cGVB_AX_UNION
% Conjecture to prove = (((eq fofType) ((cGVB_UNION x) y)) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):Prop
% We need to prove ['(((eq fofType) ((cGVB_UNION x) y)) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))']
% Parameter fofType:Type.
% Parameter y:fofType.
% Parameter x:fofType.
% Parameter cGVB_COMPLEMENT:(fofType->fofType).
% Parameter cGVB_INTERSECT:(fofType->(fofType->fofType)).
% Parameter cGVB_UNION:(fofType->(fofType->fofType)).
% Trying to prove (((eq fofType) ((cGVB_UNION x) y)) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P ((cGVB_UNION x) y))
% Found (fun (x01:(P ((cGVB_UNION x) y)))=> x01) as proof of (P ((cGVB_UNION x) y))
% Found (fun (x01:(P ((cGVB_UNION x) y)))=> x01) as proof of (P0 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P ((cGVB_UNION x) y))
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P0 b)
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((cGVB_UNION x) y))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((cGVB_UNION x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found x02:(P ((cGVB_UNION x) y))
% Found (fun (x02:(P ((cGVB_UNION x) y)))=> x02) as proof of (P ((cGVB_UNION x) y))
% Found (fun (x02:(P ((cGVB_UNION x) y)))=> x02) as proof of (P0 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) 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 x01:(P ((cGVB_UNION x) y))
% Found (fun (x01:(P ((cGVB_UNION x) y)))=> x01) as proof of (P ((cGVB_UNION x) y))
% Found (fun (x01:(P ((cGVB_UNION x) y)))=> x01) as proof of (P0 ((cGVB_UNION x) y))
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P0 b)
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((cGVB_UNION x) y))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((cGVB_UNION x) y)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found x02:(P ((cGVB_UNION x) y))
% Found (fun (x02:(P ((cGVB_UNION x) y)))=> x02) as proof of (P ((cGVB_UNION x) y))
% Found (fun (x02:(P ((cGVB_UNION x) y)))=> x02) as proof of (P0 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P ((cGVB_UNION x) y))
% Instantiate: a:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_UNION x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_UNION x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_UNION x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_UNION x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: a:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) 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 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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:(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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0 as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found x0:(P0 ((cGVB_UNION x) y))
% Found (fun (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of ((P0 ((cGVB_UNION x) y))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of (P ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 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 x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of ((P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Instantiate: a:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_UNION x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_UNION x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P2 b)
% Instantiate: b:=((cGVB_UNION x) y):fofType
% Found (fun (x0:(P2 b))=> x0) as proof of (P2 ((cGVB_UNION x) y))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 ((cGVB_UNION x) y)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b)
% Found x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: a:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: a:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P b)
% Found x0 as proof of (P0 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0 as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0 as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0 as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found x0:(P0 ((cGVB_UNION x) y))
% Found (fun (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of ((P0 ((cGVB_UNION x) y))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of (P ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found x0:(P0 ((cGVB_UNION x) y))
% Found (fun (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of ((P0 ((cGVB_UNION x) y))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 ((cGVB_UNION x) y)))=> x0) as proof of (P ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> 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 eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of ((P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of ((P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=((cGVB_UNION 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 x00:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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) 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 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 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 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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) 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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) 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 x0:(P1 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P1 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x01:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x01) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x02:(P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x02) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P1 b)
% Found x0 as proof of (P2 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P1 b)
% Found x0 as proof of (P2 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: a:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 x0:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: a:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found (fun (x00:(P2 b0))=> x00) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b0))=> x00) as proof of ((P2 b0)->(P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION 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_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of ((P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))->(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x0) as proof of (P (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b1)
% Found x00:(P1 ((cGVB_UNION x) y))
% Instantiate: b0:=((cGVB_UNION x) y):fofType
% Found x00 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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 eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P b0)
% Found x0 as proof of (P0 ((cGVB_UNION x) y))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x00:(P2 ((cGVB_UNION x) y))
% Instantiate: b0:=((cGVB_UNION x) y):fofType
% Found (fun (x00:(P2 ((cGVB_UNION x) y)))=> x00) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 ((cGVB_UNION x) y)))=> x00) as proof of ((P2 ((cGVB_UNION x) y))->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 ((cGVB_UNION x) y)))=> x00) as proof of (P1 b0)
% Found x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (fun (x000:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))))=> x000) as proof of (P2 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_UNION 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_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=((cGVB_UNION 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_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found x0:(P1 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((cGVB_UNION x) y)):(((eq fofType) ((cGVB_UNION x) y)) ((cGVB_UNION x) y))
% Found (eq_ref0 ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found ((eq_ref fofType) ((cGVB_UNION x) y)) as proof of (((eq fofType) ((cGVB_UNION x) y)) b0)
% Found eq_ref00:=(eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))):(((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Found (eq_ref0 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) b00)
% Found ((eq_ref fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y)))) as proof of (((eq fofType) (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT 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:(P1 (cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))))
% Instantiate: b0:=(cGVB_COMPLEMENT ((cGVB_INTERSECT (cGVB_COMPLEMENT x)) (cGVB_COMPLEMENT y))):fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of ((
% EOF
%------------------------------------------------------------------------------