%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV093^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n089.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 13:33:43 EDT 2014

% Result   : Timeout 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV093^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.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 08:01:26 CDT 2014
% % CPUTime  : 300.03 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (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)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 cT146_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)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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.
% 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)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 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:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 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:(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:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of (((Xr Xx0) Xy0)->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x3:((Xr Xx0) Xy0)) (x20:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x1 Xx0) Xy0) x3)) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (x2:((Xr Xx0) Xy0)) (x10:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x200:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x10 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x10 Xx0) Xy0) x2)) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((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 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 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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x2) x00)) ((Xp Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->((Xp0 Xx0) Xy0))
% Found (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((x2 Xx0) Xy0) x1)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->((Xp0 Xx0) Xy0)))
% Found (and_rect00 (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((x2 Xx0) Xy0) x1)))) as proof of (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))))=> (((fun (P:Type) (x2:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x2) x00)) ((Xp0 Xx0) Xy0)) (fun (x2:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x3:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw))))->((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:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))
% Found (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((x3 Xx0) Xy0) x2)) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))
% Found (and_rect00 (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) P) x3) x0)) ((Xp Xx0) Xy0)) (fun (x3:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (x4:(forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))=> (((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 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 ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx0)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))))
% 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 ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))))
% 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 ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))))
% 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 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 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 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 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 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 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 x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xx0) Xv)
% Found (x100 x4) as proof of ((Xp Xx0) Xv)
% Found ((x10 Xv) x4) as proof of ((Xp Xx0) Xv)
% Found (((x1 Xx0) Xv) x4) as proof of ((Xp Xx0) Xv)
% Found (((x1 Xx0) Xv) x4) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xu) Xy0)
% 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 ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx0)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))))
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x5 as proof of ((Xp Xx0) Xv)
% 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 ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))))
% Found x40:=(x4 x20):((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x20) as proof of ((Xp Xu) Xy0)
% Found (x4 x20) as proof of ((Xp Xu) Xy0)
% Found x40:=(x4 x20):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x4 x20) as proof of ((Xp Xx0) Xv)
% Found (x4 x20) 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 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 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 ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx0)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))))
% 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 x3:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x3 as proof of ((Xp Xu) Xy0)
% Found x3:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x3 as proof of ((Xp Xx0) Xv)
% 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 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 x40:=(x4 x20):((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x20) as proof of ((Xp Xu) Xy0)
% Found (x4 x20) as proof of ((Xp Xu) Xy0)
% Found x40:=(x4 x20):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x4 x20) as proof of ((Xp Xx0) Xv)
% Found (x4 x20) as proof of ((Xp Xx0) Xv)
% Found x20:=(x2 x00):((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x2 x00) as proof of ((Xp Xu) Xy0)
% Found (x2 x00) as proof of ((Xp Xu) Xy0)
% Found x20:=(x2 x00):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x2 x00) as proof of ((Xp Xx0) Xv)
% Found (x2 x00) as proof of ((Xp Xx0) Xv)
% Found x40:=(x4 x00):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x4 x00) as proof of ((Xp Xx0) Xv)
% Found (x4 x00) as proof of ((Xp Xx0) Xv)
% Found x40:=(x4 x00):((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x00) as proof of ((Xp Xu) Xy0)
% Found (x4 x00) as proof of ((Xp Xu) 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 x1000:=(x100 x6):((Xp Xy0) Xw)
% Found (x100 x6) as proof of ((Xp Xy0) Xw)
% Found ((x10 Xw) x6) as proof of ((Xp Xy0) Xw)
% Found (((x1 Xy0) Xw) x6) as proof of ((Xp Xy0) Xw)
% Found (((x1 Xy0) Xw) x6) as proof of ((Xp Xy0) Xw)
% Found ((conj20 x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xu) Xy0)) ((Xp Xy0) Xw))
% Found (((conj2 ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xu) Xy0)) ((Xp Xy0) Xw))
% Found ((((conj ((Xp Xu) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xu) Xy0)) ((Xp Xy0) Xw))
% Found ((((conj ((Xp Xu) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xu) Xy0)) ((Xp Xy0) Xw))
% Found (x2000 ((((conj ((Xp Xu) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6))) as proof of ((Xp Xu) Xw)
% Found ((x200 Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xu) Xw)
% Found (((fun (Xy0:fofType)=> ((x20 Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xu) Xw)
% Found (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xu) Xw)
% Found (fun (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of ((Xp Xu) Xw)
% Found (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of (((Xr Xv) Xw)->((Xp Xu) Xw))
% Found (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of (((Xp Xu) Xv)->(((Xr Xv) Xw)->((Xp Xu) Xw)))
% Found (and_rect10 (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xu) Xw)
% Found ((and_rect1 ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xu) Xw)
% Found (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xu) Xw)
% Found (fun (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of ((Xp Xu) Xw)
% Found (fun (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))
% Found (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (forall (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))
% Found ((conj10 x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))
% Found (((conj1 (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))
% Found ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))
% Found ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))
% Found (x3 ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))) as proof of ((Xp Xx) Xy)
% Found ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xy))
% Found (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((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 (and_rect00 (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found ((and_rect0 ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found (((fun (P:Type) (x1:((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) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x0:((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)))))=> (((fun (P:Type) (x1:((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) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (Xp:(fofType->(fofType->Prop))) (x0:((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)))))=> (((fun (P:Type) (x1:((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) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) 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))))->((Xp Xx) Xy))
% Found (fun (x:(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xx) Xy)))) (Xp:(fofType->(fofType->Prop))) (x0:((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)))))=> (((fun (P:Type) (x1:((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) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of (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 (fun (x:(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xx) Xy)))) (Xp:(fofType->(fofType->Prop))) (x0:((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)))))=> (((fun (P:Type) (x1:((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) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xp) ((((conj (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))) x1) (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xu) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xu) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xu) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xu) Xw)) (fun (x5:((Xp Xu) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xu) Xy0) Xw)) Xv) ((((conj ((Xp Xu) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of ((forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((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 x300:=(x30 x200):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x30 x200) as proof of ((Xp Xx0) Xv)
% Found ((x3 x10) x200) as proof of ((Xp Xx0) Xv)
% Found ((x3 x10) x200) as proof of ((Xp Xx0) Xv)
% Found x40:=(x4 x00):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x4 x00) as proof of ((Xp Xx0) Xv)
% Found (x4 x00) as proof of ((Xp Xx0) Xv)
% Found x4:((Xp0 Xu) Xz)
% Found (fun (x5:((Xr Xv) Xw))=> x4) as proof of ((Xp0 Xu) Xz)
% Found (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xz))
% Found (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4) as proof of (((Xp0 Xu) Xz)->(((Xr Xv) Xw)->((Xp0 Xu) Xz)))
% Found (and_rect10 (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4)) as proof of ((Xp0 Xu) Xz)
% Found ((and_rect1 ((Xp0 Xu) Xz)) (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4)) as proof of ((Xp0 Xu) Xz)
% Found (((fun (P:Type) (x4:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4)) as proof of ((Xp0 Xu) Xz)
% Found (fun (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4))) as proof of ((Xp0 Xu) Xz)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4))) as proof of (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((Xp0 Xu) Xz)) (x5:((Xr Xv) Xw))=> x4))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found x300:=(x30 x200):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x30 x200) as proof of ((Xp Xx0) Xv)
% Found ((x3 x10) x200) as proof of ((Xp Xx0) Xv)
% Found ((x3 x10) x200) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x6:((Xp Xy0) Xz))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x6:((Xp Xy0) Xz))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x6:((Xp Xy0) Xz))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x6:((Xp Xy0) Xz))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x6:((Xp Xy0) Xz))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x6:((Xp Xy0) Xz))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found x40:=(x4 x20):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x4 x20) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))=> (x4 x20)) as proof of ((Xp Xx0) Xv)
% Found (fun (x4:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) (x5:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))=> (x4 x20)) as proof of (((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))->((Xp Xx0) Xv))
% Found (fun (x4:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) (x5:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))=> (x4 x20)) as proof of (((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))->(((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x4:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) (x5:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))=> (x4 x20))) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x4:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) (x5:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))=> (x4 x20))) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x4:(((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))->(((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))) P) x4) x3)) ((Xp Xx0) Xv)) (fun (x4:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) (x5:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))=> (x4 x20))) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x4:(((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))->(((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) ((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))) P) x4) x3)) ((Xp Xx0) Xv)) (fun (x4:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0))) (x5:((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))=> (x4 x20))) as proof of ((Xp Xx0) Xv)
% Found x40:=(x4 x00):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x4 x00) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz)))=> (x4 x00)) as proof of ((Xp Xx0) Xv)
% Found (fun (x4:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (x5:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz)))=> (x4 x00)) as proof of ((((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz))->((Xp Xx0) Xv))
% Found (fun (x4:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (x5:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz)))=> (x4 x00)) as proof of ((((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))->((((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz))->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x4:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (x5:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz)))=> (x4 x00))) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x4:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (x5:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz)))=> (x4 x00))) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x4:((((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))->((((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz))) P) x4) x1)) ((Xp Xx0) Xv)) (fun (x4:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (x5:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz)))=> (x4 x00))) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x4:((((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))->((((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz))) P) x4) x1)) ((Xp Xx0) Xv)) (fun (x4:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xx0) Xy0))) (x5:(((and (forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))) (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw))))->((Xp Xy0) Xz)))=> (x4 x00))) as proof of ((Xp Xx0) Xv)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x6:((Xp Xy0) Xz))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5) as proof of (((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x2)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy0)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)) P) x5) x2)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xy0)) (x6:((Xp Xy0) Xz))=> x5)) as proof of ((Xp Xx0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv)
% Found x300:=(x30 x200):((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (x30 x200) as proof of ((Xp Xx0) Xv)
% Found ((x3 x10) x200) as proof of ((Xp Xx0) Xv)
% Found (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))))=> ((x3 x10) x200)) as proof of ((Xp Xx0) Xv)
% Found (fun (x3:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))))=> ((x3 x10) x200)) as proof of (((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))->((Xp Xx0) Xv))
% Found (fun (x3:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))))=> ((x3 x10) x200)) as proof of (((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))->(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x3:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))))=> ((x3 x10) x200))) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x3:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))))=> ((x3 x10) x200))) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x3:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))->(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))) P) x3) x2)) ((Xp Xx0) Xv)) (fun (x3:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))))=> ((x3 x10) x200))) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x3:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))->(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp Xu) Xv)) ((Xr Xv) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz)))) P) x3) x2)) ((Xp Xx0) Xv)) (fun (x3:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xx0) Xy0)))) (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp Xu) Xv0)) ((Xr Xv0) Xw))->((Xp Xu) Xw)))->((Xp Xy0) Xz))))=> ((x3 x10) x200))) as proof of ((Xp Xx0) Xv)
% Found x50:=(x5 Xx00):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (x5 Xx00) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xx0) Xv)
% Found (x100 x4) as proof of ((Xp Xx0) Xv)
% Found ((x10 Xv) x4) as proof of ((Xp Xx0) Xv)
% Found (((x1 Xx0) Xv) x4) as proof of ((Xp Xx0) Xv)
% Found (fun (x4:((Xr Xx0) Xy0))=> (((x1 Xx0) Xv) x4)) as proof of ((Xp Xx0) Xv)
% Found x50:=(x5 Xx00):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (x5 Xx00) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw))))
% Found x6:((Xp0 Xu) Xz)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xz)
% Found (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xz))
% Found (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xz)->(((Xr Xv) Xw)->((Xp0 Xu) Xz)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found ((and_rect2 ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found (fun (x20:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xz)
% Found (fun (Xw:fofType) (x20:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz))
% Found (fun (Xv:fofType) (Xw:fofType) (x20:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x20:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x20:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found x30:=(x3 Xx00):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (x3 Xx00) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx00)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x3 Xx00)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw))))
% Found x6:((Xp0 Xu) Xz)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xz)
% Found (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xz))
% Found (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xz)->(((Xr Xv) Xw)->((Xp0 Xu) Xz)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found ((and_rect2 ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found (fun (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xz)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found x50:=(x5 Xx00):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (x5 Xx00) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw))))
% Found x6:((Xp0 Xu) Xz)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xz)
% Found (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xz))
% Found (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xz)->(((Xr Xv) Xw)->((Xp0 Xu) Xz)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found ((and_rect2 ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xz)
% Found (fun (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xz)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xz)) (fun (x6:((Xp0 Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xz)) ((Xr Xv) Xw))->((Xp0 Xu) Xz)))
% Found x50:=(x5 Xx00):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (x5 Xx00) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x5 Xx00)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw))))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x50:=(x5 x500):((Xp0 Xu) Xz)
% Found (x5 x500) as proof of ((Xp0 Xu) Xz)
% Found (fun (x6:((Xr Xv) Xw))=> (x5 x500)) as proof of ((Xp0 Xu) Xz)
% Found (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xz))
% Found (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)) as proof of (((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->((Xp0 Xu) Xz)))
% Found (and_rect20 (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500))) as proof of ((Xp0 Xu) Xz)
% Found ((and_rect2 ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500))) as proof of ((Xp0 Xu) Xz)
% Found (((fun (P:Type) (x5:(((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw)) P) x5) x200)) ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500))) as proof of ((Xp0 Xu) Xz)
% Found (fun (x500:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x5:(((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw)) P) x5) x200)) ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)))) as proof of ((Xp0 Xu) Xz)
% Found (fun (x200:((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))) (x500:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x5:(((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw)) P) x5) x200)) ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)))) as proof of ((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))
% Found (fun (Xw:fofType) (x200:((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))) (x500:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x5:(((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw)) P) x5) x200)) ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)))) as proof of (((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))) (x500:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x5:(((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw)) P) x5) x200)) ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)))) as proof of (forall (Xw:fofType), (((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))) (x500:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x5:(((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw)) P) x5) x200)) ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))) (x500:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x5:(((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw)) P) x5) x200)) ((Xp0 Xu) Xz)) (fun (x5:((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))) (x6:((Xr Xv) Xw))=> (x5 x500)))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz))) ((Xr Xv) Xw))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))))
% Found x5000:=(x500 Xx00):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (x500 Xx00) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x500 Xx00)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x500 Xx00)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw))))
% Found x6:((Xr Xu) Xz)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xr Xu) Xz)
% Found (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xr Xu) Xz))
% Found (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xu) Xz)->(((Xr Xv) Xw)->((Xr Xu) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found ((and_rect2 ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found (fun (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xr Xu) Xz)
% Found (fun (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz))
% Found (fun (Xv:fofType) (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found x6:((Xr Xu) Xz)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xr Xu) Xz)
% Found (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xr Xu) Xz))
% Found (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xu) Xz)->(((Xr Xv) Xw)->((Xr Xu) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found ((and_rect2 ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found (fun (x200:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xr Xu) Xz)
% Found (fun (Xw:fofType) (x200:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x200)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found x6:((Xr Xv) Xz)
% Found (fun (x6:((Xr Xv) Xz))=> x6) as proof of ((Xr Xv) Xz)
% Found (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6) as proof of (((Xr Xv) Xz)->((Xr Xv) Xz))
% Found (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6) as proof of (((Xr Xv) Xy0)->(((Xr Xv) Xz)->((Xr Xv) Xz)))
% Found (and_rect10 (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found ((and_rect1 ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found (fun (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of ((Xr Xv) Xz)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (forall (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz))))
% Found x5:((Xp Xx0) Xv)
% Found (fun (x6:((Xp Xy0) Xv))=> x5) as proof of ((Xp Xx0) Xv)
% Found (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5) as proof of (((Xp Xy0) Xv)->((Xp Xx0) Xv))
% Found (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5) as proof of (((Xp Xx0) Xv)->(((Xp Xy0) Xv)->((Xp Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect1 ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xv)->(((Xp Xy0) Xv)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xp Xy0) Xv)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5)) as proof of ((Xp Xx0) Xv)
% Found (fun (x4:((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xv)->(((Xp Xy0) Xv)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xp Xy0) Xv)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5))) as proof of ((Xp Xx0) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xv)->(((Xp Xy0) Xv)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xp Xy0) Xv)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5))) as proof of (((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv))->((Xp Xx0) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xv)->(((Xp Xy0) Xv)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xp Xy0) Xv)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5))) as proof of (fofType->(((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv))->((Xp Xx0) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xv)->(((Xp Xy0) Xv)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xp Xy0) Xv)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv))->((Xp Xx0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xv)->(((Xp Xy0) Xv)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xp Xy0) Xv)) P) x5) x4)) ((Xp Xx0) Xv)) (fun (x5:((Xp Xx0) Xv)) (x6:((Xp Xy0) Xv))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xp Xx0) Xv)) ((Xp Xy0) Xv))->((Xp Xx0) Xv))))
% Found x6:((Xr Xu) Xz)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xr Xu) Xz)
% Found (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xr Xu) Xz))
% Found (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xu) Xz)->(((Xr Xv) Xw)->((Xr Xu) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found ((and_rect2 ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xr Xu) Xz)
% Found (fun (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xr Xu) Xz)
% Found (fun (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz))
% Found (fun (Xv:fofType) (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x201:((and ((Xr Xu) Xz)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xr Xu) Xz)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xr Xu) Xz)) ((Xr Xv) Xw)) P) x6) x201)) ((Xr Xu) Xz)) (fun (x6:((Xr Xu) Xz)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xr Xu) Xz)) ((Xr Xv) Xw))->((Xr Xu) Xz)))
% Found x401:=(x40 x50):((Xp0 Xu) Xz)
% Found (x40 x50) as proof of ((Xp0 Xu) Xz)
% Found ((x4 x400) x50) as proof of ((Xp0 Xu) Xz)
% Found (fun (x5:((Xr Xv) Xw))=> ((x4 x400) x50)) as proof of ((Xp0 Xu) Xz)
% Found (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xz))
% Found (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)) as proof of (((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->((Xp0 Xu) Xz)))
% Found (and_rect20 (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50))) as proof of ((Xp0 Xu) Xz)
% Found ((and_rect2 ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50))) as proof of ((Xp0 Xu) Xz)
% Found (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50))) as proof of ((Xp0 Xu) Xz)
% Found (fun (x50:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)))) as proof of ((Xp0 Xu) Xz)
% Found (fun (x400:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x50:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)))) as proof of ((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))
% Found (fun (x200:((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))) (x400:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x50:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)))) as proof of ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))
% Found (fun (Xw:fofType) (x200:((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))) (x400:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x50:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)))) as proof of (((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz))))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))) (x400:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x50:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)))) as proof of (forall (Xw:fofType), (((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))) (x400:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x50:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))) (x400:(forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))) (x50:(forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0))))=> (((fun (P:Type) (x4:(((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))->(((Xr Xv) Xw)->P)))=> (((((and_rect ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xz)) (fun (x4:((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))) (x5:((Xr Xv) Xw))=> ((x4 x400) x50)))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv0:fofType) (Xw:fofType), (((and ((Xp0 Xu0) Xv0)) ((Xr Xv0) Xw))->((Xp0 Xu0) Xw)))->((Xp0 Xu) Xz)))) ((Xr Xv) Xw))->((forall (Xx00:fofType) (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00)))->((forall (Xu0:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu0) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu0) Xw0)))->((Xp0 Xu) Xz)))))
% Found x500:=(x50 Xx00):(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (x50 Xx00) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x50 Xx00)) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw)))
% Found (fun (Xu:fofType)=> (x50 Xx00)) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx00) Xv)) ((Xr Xv) Xw))->((Xp0 Xx00) Xw))))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x8:((Xr Xv) Xz)
% Found x8 as proof of ((Xr Xv) Xz)
% Found x7:((Xp Xx0) Xv)
% Found x7 as proof of ((Xp Xx0) Xv)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x50000:=(x5000 x20):((Xp0 Xx0) Xw)
% Found (x5000 x20) as proof of ((Xp0 Xx0) Xw)
% Found ((x500 Xv) x20) as proof of ((Xp0 Xx0) Xw)
% Found (((fun (Xv0:fofType)=> ((x50 Xv0) Xw)) Xv) x20) as proof of ((Xp0 Xx0) Xw)
% Found (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20) as proof of ((Xp0 Xx0) Xw)
% Found (fun (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)) as proof of ((Xp0 Xx0) Xw)
% Found (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)) as proof of ((forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0)))->((Xp0 Xx0) Xw))
% Found (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)) as proof of ((forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))->((forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0)))->((Xp0 Xx0) Xw)))
% Found (and_rect10 (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20))) as proof of ((Xp0 Xx0) Xw)
% Found ((and_rect1 ((Xp0 Xx0) Xw)) (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20))) as proof of ((Xp0 Xx0) Xw)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x4) x00)) ((Xp0 Xx0) Xw)) (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20))) as proof of ((Xp0 Xx0) Xw)
% Found (fun (x20:((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x4) x00)) ((Xp0 Xx0) Xw)) (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)))) as proof of ((Xp0 Xx0) Xw)
% Found (fun (Xw:fofType) (x20:((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x4) x00)) ((Xp0 Xx0) Xw)) (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)))) as proof of (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))
% Found (fun (Xv:fofType) (Xw:fofType) (x20:((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x4) x00)) ((Xp0 Xx0) Xw)) (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x20:((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x4) x00)) ((Xp0 Xx0) Xw)) (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x20:((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))->((forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))->P)))=> (((((and_rect (forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw))->((Xp0 Xu) Xw)))) P) x4) x00)) ((Xp0 Xx0) Xw)) (fun (x4:(forall (Xx00:fofType) (Xy0:fofType), (((Xr Xx00) Xy0)->((Xp0 Xx00) Xy0)))) (x5:(forall (Xu:fofType) (Xv:fofType) (Xw0:fofType), (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xw0))->((Xp0 Xu) Xw0))))=> (((fun (Xv0:fofType)=> (((x5 Xx0) Xv0) Xw)) Xv) x20)))) as proof of (fofType->(forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xx0) Xv)) ((Xr Xv) Xw))->((Xp0 Xx0) Xw))))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x4:((Xp0 Xu) Xy00)
% Found (fun (x5:((Xr Xv) Xw))=> x4) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4) as proof of (((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect10 (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4)) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect1 ((Xp0 Xu) Xy00)) (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4)) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x4:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4))) as proof of (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x4:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:((Xp0 Xu) Xy00)) (x5:((Xr Xv) Xw))=> x4))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found x40:=(x4 x201):((Xp0 Xu) Xy00)
% Found (x4 x201) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x5:((Xr Xv) Xw))=> (x4 x201)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)) as proof of ((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect10 (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201))) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect1 ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201))) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x4:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)))) as proof of (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))
% Found (fun (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)))) as proof of (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)))) as proof of (forall (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x5:((Xr Xv) Xw))=> (x4 x201)))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x20 as proof of ((Xr Xx00) Xv)
% Found (x210 x20) as proof of ((Xp0 Xx00) Xv)
% Found ((x21 Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found (((x2 Xx00) Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found (((x2 Xx00) Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found x200:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x200 as proof of ((Xr Xx00) Xv)
% Found (x40000 x200) as proof of ((Xp0 Xx00) Xv)
% Found ((x4000 Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x400 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x400 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found x200:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x200 as proof of ((Xr Xx00) Xv)
% Found (x400 x200) as proof of ((Xp0 Xx00) Xv)
% Found ((x40 Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found x200:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x200 as proof of ((Xr Xx00) Xv)
% Found (x400 x200) as proof of ((Xp0 Xx00) Xv)
% Found ((x40 Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found x200:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x200 as proof of ((Xr Xx00) Xv)
% Found (x400 x200) as proof of ((Xp0 Xx00) Xv)
% Found ((x40 Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x7:((Xr Xv0) Xw))=> x6) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6) as proof of (((Xr Xv0) Xw)->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz)))
% Found (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6) as proof of (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found ((and_rect2 ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz)))
% Found (fun (Xv0:fofType) (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xu:fofType) (Xv0:fofType) (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xv0:fofType) (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xu:fofType) (Xv0:fofType) (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x20 as proof of ((Xr Xx00) Xv)
% Found (x210 x20) as proof of ((Xp0 Xx00) Xv)
% Found ((x21 Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found (((x2 Xx00) Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found (((x2 Xx00) Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x7:((Xr Xv0) Xw))=> x6) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6) as proof of (((Xr Xv0) Xw)->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz)))
% Found (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6) as proof of (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found ((and_rect2 ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x200)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x200:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x200)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (Xw:fofType) (x200:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x200)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz)))
% Found (fun (Xv0:fofType) (Xw:fofType) (x200:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x200)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xu:fofType) (Xv0:fofType) (Xw:fofType) (x200:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x200)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xv0:fofType) (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xu:fofType) (Xv0:fofType) (Xw:fofType) (x200:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x200)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found x200:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x200 as proof of ((Xr Xx00) Xv)
% Found (x400 x200) as proof of ((Xp0 Xx00) Xv)
% Found ((x40 Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found x400:=(x40 x201):((Xp0 Xu) Xy00)
% Found (x40 x201) as proof of ((Xp0 Xu) Xy00)
% Found ((x4 Xy00) x201) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)) as proof of ((forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect10 (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201))) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect1 ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201))) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (Xy00:fofType) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)))) as proof of (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))
% Found (fun (x200:((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))) (Xy00:fofType) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)))) as proof of (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))
% Found (fun (Xw:fofType) (x200:((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))) (Xy00:fofType) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)))) as proof of (((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))->(forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))) (Xy00:fofType) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)))) as proof of (forall (Xw:fofType), (((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))->(forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))) (Xy00:fofType) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))->(forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))) (Xy00:fofType) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))->(((Xr Xv) Xw)->P)))=> (((((and_rect (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw)) P) x4) x200)) ((Xp0 Xu) Xy00)) (fun (x4:(forall (Xy000:fofType), (((Xr Xx00) Xy000)->((Xp0 Xu) Xy000)))) (x5:((Xr Xv) Xw))=> ((x4 Xy00) x201)))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and (forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))) ((Xr Xv) Xw))->(forall (Xy00:fofType), (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))))
% Found x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x7:((Xr Xv0) Xw))=> x6) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6) as proof of (((Xr Xv0) Xw)->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz)))
% Found (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6) as proof of (((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found ((and_rect2 ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6)) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))
% Found (fun (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz)))
% Found (fun (Xv0:fofType) (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xu:fofType) (Xv0:fofType) (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xv0:fofType) (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xu:fofType) (Xv0:fofType) (Xw:fofType) (x20:((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)))=> (((fun (P:Type) (x6:(((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))->(((Xr Xv0) Xw)->P)))=> (((((and_rect ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw)) P) x6) x20)) ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (fun (x6:((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) (x7:((Xr Xv0) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv0:fofType) (Xw:fofType), (((and ((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))) ((Xr Xv0) Xw))->((and ((Xp0 Xu) Xv)) ((Xr Xv) Xz))))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x20 as proof of ((Xr Xx00) Xv)
% Found (x210 x20) as proof of ((Xp0 Xx00) Xv)
% Found ((x21 Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found (((x2 Xx00) Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found (((x2 Xx00) Xv) x20) as proof of ((Xp0 Xx00) Xv)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found (fun (x20:((Xr Xx00) Xy00))=> x20) as proof of ((Xr Xv) Xy00)
% Found (fun (Xy00:fofType) (x20:((Xr Xx00) Xy00))=> x20) as proof of (((Xr Xx00) Xy00)->((Xr Xv) Xy00))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found (fun (x20:((Xr Xx00) Xy00))=> x20) as proof of ((Xr Xv) Xy00)
% Found (fun (Xy00:fofType) (x20:((Xr Xx00) Xy00))=> x20) as proof of (((Xr Xx00) Xy00)->((Xr Xv) Xy00))
% Found x200:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xy00:fofType
% Found x200 as proof of ((Xr Xx00) Xv)
% Found (x400 x200) as proof of ((Xp0 Xx00) Xv)
% Found ((x40 Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found (((x4 Xx00) Xv) x200) as proof of ((Xp0 Xx00) Xv)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x200:=(x20 Xy00):(((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00))
% Found (x20 Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x2 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x2 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found x400:=(x40 Xy00):(((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00))
% Found (x40 Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x4 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x4 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found (fun (x20:((Xr Xx00) Xy00))=> x20) as proof of ((Xr Xv) Xy00)
% Found (fun (Xy00:fofType) (x20:((Xr Xx00) Xy00))=> x20) as proof of (((Xr Xx00) Xy00)->((Xr Xv) Xy00))
% Found x8:((Xr Xv) Xz)
% Found (fun (x8:((Xr Xv) Xz))=> x8) as proof of ((Xr Xv) Xz)
% Found (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8) as proof of (((Xr Xv) Xz)->((Xr Xv) Xz))
% Found (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8) as proof of (((Xp Xy0) Xv)->(((Xr Xv) Xz)->((Xr Xv) Xz)))
% Found (and_rect20 (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)) as proof of ((Xr Xv) Xz)
% Found ((and_rect2 ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)) as proof of ((Xr Xv) Xz)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)) as proof of ((Xr Xv) Xz)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)) as proof of ((Xr Xv) Xz)
% Found x7:((Xp Xx0) Xv)
% Found (fun (x8:((Xr Xv) Xy0))=> x7) as proof of ((Xp Xx0) Xv)
% Found (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7) as proof of (((Xr Xv) Xy0)->((Xp Xx0) Xv))
% Found (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7) as proof of (((Xp Xx0) Xv)->(((Xr Xv) Xy0)->((Xp Xx0) Xv)))
% Found (and_rect20 (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7)) as proof of ((Xp Xx0) Xv)
% Found ((and_rect2 ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7)) as proof of ((Xp Xx0) Xv)
% Found (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7)) as proof of ((Xp Xx0) Xv)
% Found ((conj20 (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found (((conj2 ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found (fun (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))) as proof of (((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->((and ((Xp Xx0) Xv)) ((Xr Xv) Xz)))
% Found (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))) as proof of (((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))->(((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))))
% Found (and_rect10 (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8))))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found ((and_rect1 ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))) (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8))))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found (((fun (P:Type) (x5:(((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))->(((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))) (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8))))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found (fun (x4:((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))->(((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))) (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))))) as proof of ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))->(((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))) (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))))) as proof of (((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))->((and ((Xp Xx0) Xv)) ((Xr Xv) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))->(((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))) (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))))) as proof of (forall (Xz:fofType), (((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))->((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))->(((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))) (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))->((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))->(((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))) (fun (x5:((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) (x6:((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))=> ((((conj ((Xp Xx0) Xv)) ((Xr Xv) Xz)) (((fun (P:Type) (x7:(((Xp Xx0) Xv)->(((Xr Xv) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xv)) ((Xr Xv) Xy0)) P) x7) x5)) ((Xp Xx0) Xv)) (fun (x7:((Xp Xx0) Xv)) (x8:((Xr Xv) Xy0))=> x7))) (((fun (P:Type) (x7:(((Xp Xy0) Xv)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xv)) ((Xr Xv) Xz)) P) x7) x6)) ((Xr Xv) Xz)) (fun (x7:((Xp Xy0) Xv)) (x8:((Xr Xv) Xz))=> x8)))))) as proof of (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((and ((Xp Xx0) Xv)) ((Xr Xv) Xy0))) ((and ((Xp Xy0) Xv)) ((Xr Xv) Xz)))->((and ((Xp Xx0) Xv)) ((Xr Xv) Xz))))
% Found x5:((Xr Xx0) Xv)
% Found (fun (x6:((Xr Xy0) Xv))=> x5) as proof of ((Xr Xx0) Xv)
% Found (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5) as proof of (((Xr Xy0) Xv)->((Xr Xx0) Xv))
% Found (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5) as proof of (((Xr Xx0) Xv)->(((Xr Xy0) Xv)->((Xr Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found ((and_rect1 ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found (fun (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of ((Xr Xx0) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))))
% Found x200:=(x20 Xy00):(((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00))
% Found (x20 Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x2 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x2 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found x6:((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found x6:((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found x6:((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% 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 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 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 x200:((Xr Xx000) Xy000)
% Instantiate: Xv:=Xx000:fofType
% Found x200 as proof of ((Xr Xv) Xy000)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x201:((Xr Xx000) Xy000)
% Instantiate: Xv:=Xx000:fofType
% Found x201 as proof of ((Xr Xv) Xy000)
% Found x201:((Xr Xx000) Xy000)
% Instantiate: Xv:=Xx000:fofType
% Found x201 as proof of ((Xr Xv) Xy000)
% Found x201:((Xr Xx000) Xy000)
% Instantiate: Xv:=Xx000:fofType
% Found x201 as proof of ((Xr Xv) Xy000)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x6:((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found x5:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xu) Xy0)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x20 as proof of ((Xr Xv) Xy00)
% Found x201:((Xr Xx000) Xy000)
% Instantiate: Xv:=Xx000:fofType
% Found x201 as proof of ((Xr Xv) Xy000)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x5 as proof of ((Xp Xx0) Xv)
% Found x20:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found (fun (x20:((Xr Xx00) Xy00))=> x20) as proof of ((Xr Xv) Xy00)
% Found (fun (Xy00:fofType) (x20:((Xr Xx00) Xy00))=> x20) as proof of (((Xr Xx00) Xy00)->((Xr Xv) Xy00))
% Found x6:((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> x6) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6) as proof of (((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x6:(((Xp0 Xu) Xy00)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp0 Xu) Xy00)) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:((Xp0 Xu) Xy00)) (x7:((Xr Xv) Xw))=> x6))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((Xp0 Xu) Xy00)) ((Xr Xv) Xw))->((Xp0 Xu) Xy00)))
% Found x5:((Xp Xu) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xu) Xy0)
% Found x60:=(x6 x200):((Xp0 Xu) Xy00)
% Found (x6 x200) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> (x6 x200)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)) as proof of ((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200))) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200))) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x20:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x200:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)))) as proof of (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))
% Found (fun (Xw:fofType) (x20:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x200:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)))) as proof of (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))
% Found (fun (Xv:fofType) (Xw:fofType) (x20:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x200:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)))) as proof of (forall (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x20:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x200:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x20:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x200:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x20)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x200)))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found x200:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x200 as proof of ((Xr Xv) Xy00)
% Found x5:((Xp Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found x5 as proof of ((Xp Xx0) Xv)
% Found x60:=(x6 x201):((Xp0 Xu) Xy00)
% Found (x6 x201) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> (x6 x201)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)) as proof of ((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201))) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201))) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))
% Found (fun (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of (forall (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found (fun (Xu:fofType) (Xv:fofType) (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))))
% Found x201:((Xr Xx00) Xy00)
% Instantiate: Xv:=Xx00:fofType
% Found x201 as proof of ((Xr Xv) Xy00)
% Found x200:=(x20 Xy00):(((Xr Xx00) Xy00)->((Xp0 Xx00) Xy00))
% Found (x20 Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x2 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% Found ((x2 Xx00) Xy00) as proof of (((Xr Xx00) Xy00)->((Xp0 Xx00) Xv))
% 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 x60:=(x6 x201):((Xp0 Xu) Xy00)
% Found (x6 x201) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x7:((Xr Xv) Xw))=> (x6 x201)) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)) as proof of (((Xr Xv) Xw)->((Xp0 Xu) Xy00))
% Found (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)) as proof of ((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->((Xp0 Xu) Xy00)))
% Found (and_rect20 (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201))) as proof of ((Xp0 Xu) Xy00)
% Found ((and_rect2 ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201))) as proof of ((Xp0 Xu) Xy00)
% Found (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of ((Xp0 Xu) Xy00)
% Found (fun (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))
% Found (fun (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))->(((Xr Xv) Xw)->P)))=> (((((and_rect (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw)) P) x6) x200)) ((Xp0 Xu) Xy00)) (fun (x6:(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) (x7:((Xr Xv) Xw))=> (x6 x201)))) as proof of (((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))->(((Xr Xx00) Xy00)->((Xp0 Xu) Xy00)))
% Found (fun (Xv:fofType) (Xw:fofType) (x200:((and (((Xr Xx00) Xy00)->((Xp0 Xu) Xy00))) ((Xr Xv) Xw))) (x201:((Xr Xx00) Xy00))
% EOF
%------------------------------------------------------------------------------