TSTP Solution File: SYO333^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYO333^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Tue Mar 29 00:51:11 EDT 2022

% Result   : Unknown 82.84s 83.05s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SYO333^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.12  % Command    : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33  % Computer   : n005.cluster.edu
% 0.12/0.33  % Model      : x86_64 x86_64
% 0.12/0.33  % CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % RAMPerCPU  : 8042.1875MB
% 0.12/0.33  % OS         : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % DateTime   : Sat Mar 12 04:30:12 EST 2022
% 0.12/0.33  % CPUTime    : 
% 0.12/0.34  ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34  Python 2.7.5
% 14.04/14.27  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 14.04/14.27  FOF formula (<kernel.Constant object at 0x2b6bf33f3b90>, <kernel.Constant object at 0x2b6bf33f3710>) of role type named u
% 14.04/14.27  Using role type
% 14.04/14.27  Declaring u:fofType
% 14.04/14.27  FOF formula (<kernel.Constant object at 0x2b6bf33f45f0>, <kernel.Single object at 0x2b6bf33f3200>) of role type named v
% 14.04/14.27  Using role type
% 14.04/14.27  Declaring v:fofType
% 14.04/14.27  FOF formula (<kernel.Constant object at 0x1fade60>, <kernel.DependentProduct object at 0x224ae18>) of role type named cDOUBLE
% 14.04/14.27  Using role type
% 14.04/14.27  Declaring cDOUBLE:(fofType->(fofType->Prop))
% 14.04/14.27  FOF formula (<kernel.Constant object at 0x2b6bf33f3200>, <kernel.DependentProduct object at 0x224ae18>) of role type named cHALF
% 14.04/14.27  Using role type
% 14.04/14.27  Declaring cHALF:(fofType->(fofType->Prop))
% 14.04/14.27  FOF formula (<kernel.Constant object at 0x2b6bf33f3b48>, <kernel.DependentProduct object at 0x224af80>) of role type named cS
% 14.04/14.27  Using role type
% 14.04/14.27  Declaring cS:(fofType->fofType)
% 14.04/14.27  FOF formula (<kernel.Constant object at 0x2b6bf33f3b90>, <kernel.Single object at 0x2b6bf33f3200>) of role type named c0
% 14.04/14.27  Using role type
% 14.04/14.27  Declaring c0:fofType
% 14.04/14.27  FOF formula (<kernel.Constant object at 0x2b6bf33f3b48>, <kernel.Single object at 0x224a830>) of role type named cSx
% 14.04/14.27  Using role type
% 14.04/14.27  Declaring cSx:fofType
% 14.04/14.27  FOF formula (((and ((and ((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))) (forall (Q:(fofType->(fofType->Prop))) (Xu0:fofType) (Xv0:fofType), (((and ((and ((and ((cHALF Xu0) Xv0)) ((Q c0) c0))) ((Q c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((Q Xx) Xy)->((Q (cS Xx)) (cS (cS Xy))))))->((Q Xu0) Xv0))))->(((cHALF u) v)->((cDOUBLE v) u))) of role conjecture named cHALF_TO_DOUBLE_1
% 14.04/14.27  Conjecture to prove = (((and ((and ((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))) (forall (Q:(fofType->(fofType->Prop))) (Xu0:fofType) (Xv0:fofType), (((and ((and ((and ((cHALF Xu0) Xv0)) ((Q c0) c0))) ((Q c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((Q Xx) Xy)->((Q (cS Xx)) (cS (cS Xy))))))->((Q Xu0) Xv0))))->(((cHALF u) v)->((cDOUBLE v) u))):Prop
% 14.04/14.27  We need to prove ['(((and ((and ((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))) (forall (Q:(fofType->(fofType->Prop))) (Xu0:fofType) (Xv0:fofType), (((and ((and ((and ((cHALF Xu0) Xv0)) ((Q c0) c0))) ((Q c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((Q Xx) Xy)->((Q (cS Xx)) (cS (cS Xy))))))->((Q Xu0) Xv0))))->(((cHALF u) v)->((cDOUBLE v) u)))']
% 14.04/14.27  Parameter fofType:Type.
% 14.04/14.27  Parameter u:fofType.
% 14.04/14.27  Parameter v:fofType.
% 14.04/14.27  Parameter cDOUBLE:(fofType->(fofType->Prop)).
% 14.04/14.27  Parameter cHALF:(fofType->(fofType->Prop)).
% 14.04/14.27  Parameter cS:(fofType->fofType).
% 14.04/14.27  Parameter c0:fofType.
% 14.04/14.27  Parameter cSx:fofType.
% 14.04/14.27  Trying to prove (((and ((and ((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))) (forall (Q:(fofType->(fofType->Prop))) (Xu0:fofType) (Xv0:fofType), (((and ((and ((and ((cHALF Xu0) Xv0)) ((Q c0) c0))) ((Q c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((Q Xx) Xy)->((Q (cS Xx)) (cS (cS Xy))))))->((Q Xu0) Xv0))))->(((cHALF u) v)->((cDOUBLE v) u)))
% 14.04/14.27  Found x9:((cDOUBLE c0) c0)
% 14.04/14.27  Found x9 as proof of ((cDOUBLE c0) c0)
% 14.04/14.27  Found x9:((cDOUBLE c0) c0)
% 14.04/14.27  Found x9 as proof of ((cDOUBLE c0) c0)
% 14.04/14.27  Found x9:((cDOUBLE c0) c0)
% 14.04/14.27  Found x9 as proof of ((cDOUBLE c0) c0)
% 14.04/14.27  Found x9:((cDOUBLE c0) c0)
% 14.04/14.27  Found x9 as proof of ((cDOUBLE c0) c0)
% 14.04/14.27  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 25.84/26.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 25.84/26.09  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found x9:((cDOUBLE c0) c0)
% 25.84/26.09  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 25.84/26.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 25.84/26.09  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.84/26.09  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found x9:((cDOUBLE c0) c0)
% 25.94/26.10  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 25.94/26.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 25.94/26.10  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found x9:((cDOUBLE c0) c0)
% 25.94/26.10  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 25.94/26.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 25.94/26.10  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 25.94/26.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found x9 as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found x9 as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found x9 as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found x9 as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found x9 as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found x9 as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 29.25/29.46  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 29.25/29.46  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found x9:((cDOUBLE c0) c0)
% 29.25/29.46  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 29.25/29.46  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 29.25/29.46  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 29.25/29.46  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found x9:((cDOUBLE c0) c0)
% 32.84/33.09  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 32.84/33.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 32.84/33.09  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found x9:((cDOUBLE c0) c0)
% 32.84/33.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found x9:((cDOUBLE c0) c0)
% 32.84/33.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found x9:((cDOUBLE c0) c0)
% 32.84/33.09  Found x9 as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found x9:((cDOUBLE c0) c0)
% 32.84/33.09  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 32.84/33.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 32.84/33.09  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.84/33.09  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found x9:((cDOUBLE c0) c0)
% 32.92/33.10  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 32.92/33.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 32.92/33.10  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found x9:((cDOUBLE c0) c0)
% 32.92/33.10  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 32.92/33.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 32.92/33.10  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found x9:((cDOUBLE c0) c0)
% 32.92/33.12  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 32.92/33.12  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 32.92/33.12  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found x9:((cDOUBLE c0) c0)
% 32.92/33.12  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 32.92/33.12  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 32.92/33.12  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 32.92/33.12  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found x9:((cDOUBLE c0) c0)
% 36.74/36.99  Found x9 as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found x9:((cDOUBLE c0) c0)
% 36.74/36.99  Found x9 as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found x9:((cDOUBLE c0) c0)
% 36.74/36.99  Found x9 as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found x9:((cDOUBLE c0) c0)
% 36.74/36.99  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 36.74/36.99  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 36.74/36.99  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 36.74/36.99  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 36.74/36.99  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 36.83/37.00  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found x9:((cDOUBLE c0) c0)
% 36.83/37.00  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 36.83/37.00  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 36.83/37.00  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 36.83/37.00  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 36.83/37.00  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.00  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.02  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.02  Found x9:((cDOUBLE c0) c0)
% 36.83/37.02  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 36.83/37.02  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 36.83/37.02  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 36.83/37.02  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.02  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.02  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.02  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.02  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 36.83/37.02  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 36.83/37.06  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.06  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.06  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.06  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 36.83/37.06  Found x9:((cDOUBLE c0) c0)
% 36.83/37.06  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 36.83/37.06  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 36.83/37.06  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 36.83/37.08  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found x9:((cDOUBLE c0) c0)
% 36.83/37.08  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 36.83/37.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 36.83/37.08  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found x9:((cDOUBLE c0) c0)
% 36.83/37.08  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 36.83/37.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 36.83/37.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 40.72/40.96  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found x9:((cDOUBLE c0) c0)
% 40.72/40.96  Found x9 as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found x9:((cDOUBLE c0) c0)
% 40.72/40.96  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 40.72/40.96  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 40.72/40.96  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 40.72/40.96  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 40.72/40.96  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 40.72/40.97  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found x9:((cDOUBLE c0) c0)
% 40.72/40.97  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 40.72/40.97  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 40.72/40.97  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 40.72/40.97  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 40.72/40.97  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.72/40.97  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found x9:((cDOUBLE c0) c0)
% 40.85/41.03  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 40.85/41.03  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 40.85/41.03  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found x9:((cDOUBLE c0) c0)
% 40.85/41.03  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 40.85/41.03  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 44.84/45.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 44.84/45.08  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found x9:((cDOUBLE c0) c0)
% 44.84/45.08  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 44.84/45.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 44.84/45.08  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found x9:((cDOUBLE c0) c0)
% 44.84/45.08  Found x9 as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found x9:((cDOUBLE c0) c0)
% 44.84/45.08  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 44.84/45.08  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 44.84/45.08  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 44.84/45.08  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 44.84/45.08  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.08  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found x9:((cDOUBLE c0) c0)
% 44.84/45.09  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 44.84/45.09  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 44.84/45.09  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 44.84/45.09  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 44.84/45.09  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.84/45.09  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.92/45.10  Found x9:((cDOUBLE c0) c0)
% 44.92/45.10  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 44.92/45.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 44.92/45.10  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 44.92/45.10  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.92/45.10  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.92/45.10  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.92/45.10  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 44.92/45.10  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 44.92/45.10  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 44.92/45.10  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.92/45.12  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.92/45.12  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.92/45.12  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 44.92/45.12  Found x9:((cDOUBLE c0) c0)
% 44.92/45.12  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 44.92/45.12  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 44.92/45.12  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 44.92/45.12  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.92/45.12  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 44.92/45.12  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.82  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.82  Found x9:((cDOUBLE c0) c0)
% 48.64/48.82  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 48.64/48.82  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 48.64/48.82  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 48.64/48.83  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 48.64/48.83  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 48.64/48.83  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found x9:((cDOUBLE c0) c0)
% 48.64/48.83  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 48.64/48.83  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 48.64/48.83  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.83  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 48.64/48.84  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 48.64/48.84  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found (fun (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((cHALF c0) (cS c0))->((cDOUBLE c0) c0))
% 48.64/48.84  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->((cDOUBLE c0) c0)))
% 48.64/48.84  Found (and_rect20 (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found ((and_rect2 ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.84  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.85  Found x9:((cDOUBLE c0) c0)
% 48.64/48.85  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 48.64/48.85  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 48.64/48.85  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 48.64/48.85  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.85  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.85  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.64/48.85  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.85  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 48.64/48.85  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 48.64/48.85  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.86  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.86  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.86  Found (fun (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.86  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((cHALF c0) (cS c0))->((cDOUBLE c0) c0))
% 48.64/48.86  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->((cDOUBLE c0) c0)))
% 48.64/48.86  Found (and_rect20 (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.86  Found ((and_rect2 ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.64/48.86  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.74/48.91  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 48.74/48.91  Found x9:((cDOUBLE c0) c0)
% 48.74/48.91  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 48.74/48.91  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 48.74/48.91  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 48.74/48.91  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.74/48.91  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.74/48.91  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 48.74/48.91  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 52.12/52.29  Found x9:((cDOUBLE c0) c0)
% 52.12/52.29  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 52.12/52.29  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 52.12/52.29  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 52.12/52.29  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 52.12/52.29  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 52.12/52.29  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 52.12/52.29  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.29  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 52.12/52.29  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 52.12/52.29  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found x9:((cDOUBLE c0) c0)
% 52.12/52.30  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 52.12/52.30  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 52.12/52.30  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 52.12/52.30  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 52.12/52.31  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 52.12/52.31  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found (fun (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((cHALF c0) (cS c0))->((cDOUBLE c0) c0))
% 52.12/52.31  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->((cDOUBLE c0) c0)))
% 52.12/52.31  Found (and_rect20 (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found ((and_rect2 ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 52.12/52.31  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found x9:((cDOUBLE c0) c0)
% 55.44/55.65  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 55.44/55.65  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 55.44/55.65  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 55.44/55.65  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 55.44/55.65  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (fun (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((cHALF c0) (cS c0))->((cDOUBLE c0) c0))
% 55.44/55.65  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->((cDOUBLE c0) c0)))
% 55.44/55.65  Found (and_rect20 (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found ((and_rect2 ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 55.44/55.65  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found x9:((cDOUBLE c0) c0)
% 58.63/58.84  Found (fun (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 58.63/58.84  Found (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9) as proof of (((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 58.63/58.84  Found (and_rect40 (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found ((and_rect4 ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (fun (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((cHALF c0) c0)->((cDOUBLE c0) c0))
% 58.63/58.84  Found (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))) as proof of (((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->((cDOUBLE c0) c0)))
% 58.63/58.84  Found (and_rect30 (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found ((and_rect3 ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (fun (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((cHALF c0) (cS c0))->((cDOUBLE c0) c0))
% 58.63/58.84  Found (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))) as proof of (((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->((cDOUBLE c0) c0)))
% 58.63/58.84  Found (and_rect20 (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.84  Found ((and_rect2 ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.85  Found (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.85  Found (fun (x4:(forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))=> (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.85  Found (fun (x3:((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (x4:(forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))=> (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))))) as proof of ((forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy)))))->((cDOUBLE c0) c0))
% 58.63/58.85  Found (fun (x3:((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (x4:(forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))=> (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9))))))) as proof of (((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))->((forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy)))))->((cDOUBLE c0) c0)))
% 58.63/58.85  Found (and_rect10 (fun (x3:((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (x4:(forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))=> (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.85  Found ((and_rect1 ((cDOUBLE c0) c0)) (fun (x3:((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (x4:(forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))=> (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))))) as proof of ((cDOUBLE c0) c0)
% 58.63/58.85  Found (((fun (P:Type) (x3:(((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))->((forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy)))))->P)))=> (((((and_rect ((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy)))))) P) x3) x1)) ((cDOUBLE c0) c0)) (fun (x3:((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (x4:(forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))=> (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))))) as proof of ((cDOUBLE c0) c0)
% 82.78/82.98  Found (((fun (P:Type) (x3:(((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))->((forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy)))))->P)))=> (((((and_rect ((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy)))))) P) x3) x1)) ((cDOUBLE c0) c0)) (fun (x3:((and ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0)))) (x4:(forall (Xx:fofType) (Xy:fofType), (((cHALF Xx) Xy)->((cHALF (cS Xx)) (cS (cS Xy))))))=> (((fun (P:Type) (x5:(((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))->(((cHALF c0) (cS c0))->P)))=> (((((and_rect ((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) ((cHALF c0) (cS c0))) P) x5) x3)) ((cDOUBLE c0) c0)) (fun (x5:((and ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0))) (x6:((cHALF c0) (cS c0)))=> (((fun (P:Type) (x7:(((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))->(((cHALF c0) c0)->P)))=> (((((and_rect ((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) ((cHALF c0) c0)) P) x7) x5)) ((cDOUBLE c0) c0)) (fun (x7:((and ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))) (x8:((cHALF c0) c0))=> (((fun (P:Type) (x9:(((cDOUBLE c0) c0)->((forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))->P)))=> (((((and_rect ((cDOUBLE c0) c0)) (forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy)))))) P) x9) x7)) ((cDOUBLE c0) c0)) (fun (x9:((cDOUBLE c0) c0)) (x10:(forall (Xx:fofType) (Xy:fofType), (((cDOUBLE Xx) Xy)->((cDOUBLE cSx) (cS (cS Xy))))))=> x9)))))))) as proof of ((cDOUBLE c0) c0)
% 82.78/82.98  % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
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