%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV143^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n183.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:48 EDT 2014

% Result   : Timeout 300.11s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV143^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n183.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:13:11 CDT 2014
% % CPUTime  : 300.11 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1941b00>, <kernel.DependentProduct object at 0x1941d40>) of role type named cTCLOSED_type
% Using role type
% Declaring cTCLOSED:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) cTCLOSED) (fun (Xp:(fofType->(fofType->Prop))) (Xs:(fofType->(fofType->Prop)))=> (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xs Xv) Xw))->((Xp Xu) Xw))))) of role definition named cTCLOSED_def
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) cTCLOSED) (fun (Xp:(fofType->(fofType->Prop))) (Xs:(fofType->(fofType->Prop)))=> (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xs Xv) Xw))->((Xp Xu) Xw)))))
% Defined: cTCLOSED:=(fun (Xp:(fofType->(fofType->Prop))) (Xs:(fofType->(fofType->Prop)))=> (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xs Xv) Xw))->((Xp Xu) Xw))))
% FOF formula (forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))->((Xp Xx) Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))))) of role conjecture named cTHM146_pme
% Conjecture to prove = (forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))->((Xp Xx) Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))->((Xp Xx) Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy)))))']
% Parameter fofType:Type.
% Definition cTCLOSED:=(fun (Xp:(fofType->(fofType->Prop))) (Xs:(fofType->(fofType->Prop)))=> (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xs Xv) Xw))->((Xp Xu) Xw)))):((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop)).
% Trying to prove (forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))->((Xp Xx) Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy)))))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x1 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2 as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0)))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp0) Xp0)->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0)))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xp))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))))
% Found x1000:=(x100 x3):((Xp Xx0) Xy0)
% Found (x100 x3) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x3) as proof of ((Xp Xx0) Xy0)
% Found (fun (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:((cTCLOSED Xp) Xr))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xp))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))))
% Found x10000:=(x1000 x2):((Xp Xx0) Xy0)
% Found (x1000 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x100 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x10 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:((cTCLOSED Xp) Xr))=> (((x10 Xx0) Xy0) x2)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))->((Xp Xx0) Xy0))))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp0 Xx00) Xy00)) ((Xp0 Xy00) Xz))->((Xp0 Xx00) Xz))))->((Xp0 Xx0) Xy0)))))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xx00:fofType) (Xy00:fofType) (Xz:fofType), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz))->((Xp Xx00) Xz))))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xr))->((Xp Xx0) Xy0))))
% Found x2000:=(x200 x1):((Xp Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp)) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:((cTCLOSED Xp) Xp))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) ((cTCLOSED Xp) Xp))->((Xp Xx0) Xy0))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xr)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xr))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xr))->((Xp0 Xx0) Xy0)))))
% Found x2000:=(x200 x1):((Xp0 Xx0) Xy0)
% Found (x200 x1) as proof of ((Xp0 Xx0) Xy0)
% Found ((x20 Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x1) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)) as proof of (((cTCLOSED Xp0) Xp0)->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found ((and_rect0 ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of ((Xp0 Xx0) Xy0)
% Found (fun (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0))
% Found (fun (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0)))
% Found (fun (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x1:((Xr Xx0) Xy0)) (Xp0:(fofType->(fofType->Prop))) (x00:((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->(((cTCLOSED Xp0) Xp0)->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0)) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:((cTCLOSED Xp0) Xp0))=> (((x2 Xx0) Xy0) x1)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->(forall (Xp0:(fofType->(fofType->Prop))), (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) ((cTCLOSED Xp0) Xp0))->((Xp0 Xx0) Xy0)))))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xp)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xp)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xp))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x3000:=(x300 x2):((Xp Xx0) Xy0)
% Found (x300 x2) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x2) as proof of ((Xp Xx0) Xy0)
% Found (fun (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of (((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->(((cTCLOSED Xp) Xr)->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect0 ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x2:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->(((cTCLOSED Xp) Xr)->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr)) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:((cTCLOSED Xp) Xr))=> (((x3 Xx0) Xy0) x2)))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x10:=(x1 Xx0):(forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:fofType), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx0) as proof of (forall (Xy00:fofType), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x30:=(x3 Xx0):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (x3 Xx0) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx0)) as proof of ((cTCLOSED (fun (x7:fofType)=> (Xp0 Xx0))) Xr)
% Found x50:=(x5 Xx0):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (x5 Xx0) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xx0)) Xu) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of ((cTCLOSED (fun (x7:fofType)=> (Xp0 Xx0))) Xr)
% Found x50:=(x5 Xu):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))
% Found (x5 Xu) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of ((cTCLOSED (fun (x7:fofType)=> (Xp0 Xu))) Xr)
% Found x50:=(x5 Xx0):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (x5 Xx0) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x50:fofType)=> (Xp0 Xx0)) Xu) Xv)) ((Xr Xv) Xw))->(((fun (x50:fofType)=> (Xp0 Xx0)) Xu) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x50:fofType)=> (Xp0 Xx0)) Xu) Xv)) ((Xr Xv) Xw))->(((fun (x50:fofType)=> (Xp0 Xx0)) Xu) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of ((cTCLOSED (fun (x50:fofType)=> (Xp0 Xx0))) Xr)
% Found x50:=(x5 Xu):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))
% Found (x5 Xu) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of ((cTCLOSED (fun (x50:fofType)=> (Xp0 Xu))) Xr)
% Found x10:=(x1 Xx0):(forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xv) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xv) Xy0)))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv) Xy0))
% Found x30:=(x3 Xu):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))
% Found (x3 Xu) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x3 Xu)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x3 Xu)) as proof of ((cTCLOSED (fun (x7:fofType)=> (Xp0 Xu))) Xr)
% Found x50:=(x5 Xu):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))
% Found (x5 Xu) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x7:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of ((cTCLOSED (fun (x7:fofType)=> (Xp0 Xu))) Xr)
% Found x50:=(x5 Xu):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))
% Found (x5 Xu) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xv)) ((Xr Xv) Xw))->(((fun (x50:fofType)=> (Xp0 Xu)) Xu0) Xw)))
% Found (fun (Xu0:fofType)=> (x5 Xu)) as proof of ((cTCLOSED (fun (x50:fofType)=> (Xp0 Xu))) Xr)
% Found x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x00 as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x100:=(x10 Xy0):(((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (x10 Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:fofType)=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x5:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xu) Xy0)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x5 as proof of ((Xp Xx0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv) Xy0))
% Found x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x00 as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x5:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xu) Xy0)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x5 as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x5 as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xu) Xy0)
% Found x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp))
% Found x00 as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xp))
% Found x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))
% Found x00 as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))
% Found x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))
% Found x00 as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) ((cTCLOSED Xp) Xr))
% Found x5:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xu) Xy0)
% Found x100:=(x10 Xy0):(((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (x10 Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found x100:=(x10 Xy0):(((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (x10 Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xv))
% Found x100:=(x10 Xy0):(((Xr Xx0) Xy0)->((Xp Xx0) Xy0))
% Found (x10 Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xv) Xy0))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xv) Xy0))
% Found ((x1 Xx0) Xy0) as proof of (((Xr Xx0) Xy0)->((Xp Xv) Xy0))
% Found (fun (Xy0:fofType)=> ((x1 Xx0) Xy0)) as proof of (((Xr Xx0) Xy0)->((Xp Xv) Xy0))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x10:=(x1 Xx0):(forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:fofType), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx0) as proof of (forall (Xy00:fofType), (((Xr Xx0) Xy00)->(
% EOF
%------------------------------------------------------------------------------