TSTP Solution File: SEV120^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV120^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n091.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 13:33:46 EDT 2014
% Result : Timeout 300.07s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV120^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n091.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 08:08:56 CDT 2014
% % CPUTime : 300.07
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x2291638>, <kernel.Type object at 0x2291950>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (S:((a->(a->Prop))->Prop)) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xz))))) of role conjecture named cTHM70_pme
% Conjecture to prove = (forall (S:((a->(a->Prop))->Prop)) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xz))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (S:((a->(a->Prop))->Prop)) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xz)))))']
% Parameter a:Type.
% Trying to prove (forall (S:((a->(a->Prop))->Prop)) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))) (S Xp))->((Xp Xx) Xz)))))
% Found x5:((Xp Xx) Xz0)
% Found (fun (x5:((Xp Xx) Xz0))=> x5) as proof of ((Xp Xx) Xz0)
% Found (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect10 (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect1 ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5)) as proof of ((Xp Xx) Xz0)
% Found (fun (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x4:((Xp Xx0) Xz)
% Found (fun (x5:((Xp Xy0) Xz))=> x4) as proof of ((Xp Xx0) Xz)
% Found (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect10 (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect1 ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4)) as proof of ((Xp Xx0) Xz)
% Found (fun (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x7:((Xp Xx) Xz0)
% Found (fun (x7:((Xp Xx) Xz0))=> x7) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x6:((Xp Xx0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x6) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x7:((Xp Xx) Xz0)
% Found (fun (x7:((Xp Xx) Xz0))=> x7) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x6:((Xp Xx0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x6) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x7:((Xp Xx) Xz0)
% Found (fun (x7:((Xp Xx) Xz0))=> x7) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x6:((Xp Xx0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x6) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x4:(S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4) as proof of ((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4) as proof of ((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (and_rect10 (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found ((and_rect1 (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x4:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x3:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (Xz0:a) (x3:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4))) as proof of (((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4))) as proof of (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:(S (fun (x50:a)=> (Xp Xx0)))) (x5:(S (fun (x50:a)=> (Xp Xy0))))=> x4))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5) as proof of ((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))
% Found (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5) as proof of ((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))
% Found (and_rect10 (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5)) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found ((and_rect1 (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5)) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5)) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (x3:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5))) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5))) as proof of (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5))) as proof of (forall (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x5:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x5))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))))
% Found x60:=(x6 x40):((Xp Xx) Xz0)
% Found (x6 x40) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)) as proof of (((S Xp)->((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)) as proof of (((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40))) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40))) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x5:(((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->P)))=> (((((and_rect ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40))) as proof of ((Xp Xx) Xz0)
% Found (fun (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->P)))=> (((((and_rect ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of ((Xp Xx) Xz0)
% Found (fun (x4:((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->P)))=> (((((and_rect ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of ((S Xp)->((Xp Xx) Xz0))
% Found (fun (Xz0:a) (x4:((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->P)))=> (((((and_rect ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))->((S Xp)->((Xp Xx) Xz0)))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->P)))=> (((((and_rect ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (forall (Xz0:a), (((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))->((S Xp)->((Xp Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->P)))=> (((((and_rect ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))->((S Xp)->((Xp Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx) Xy0))->(((S Xp)->((Xp Xx) Xz0))->P)))=> (((((and_rect ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((S Xp)->((Xp Xx) Xy0))) (x6:((S Xp)->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((S Xp)->((Xp Xx) Xy0))) ((S Xp)->((Xp Xx) Xz0)))->((S Xp)->((Xp Xx) Xz0)))))
% Found x50:=(x5 x40):((Xp Xx0) Xz)
% Found (x5 x40) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)) as proof of (((S Xp)->((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)) as proof of (((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40))) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40))) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x5:(((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->P)))=> (((((and_rect ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40))) as proof of ((Xp Xx0) Xz)
% Found (fun (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->P)))=> (((((and_rect ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of ((Xp Xx0) Xz)
% Found (fun (x4:((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->P)))=> (((((and_rect ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of ((S Xp)->((Xp Xx0) Xz))
% Found (fun (Xz0:a) (x4:((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->P)))=> (((((and_rect ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))->((S Xp)->((Xp Xx0) Xz)))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->P)))=> (((((and_rect ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (a->(((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))->((S Xp)->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->P)))=> (((((and_rect ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (forall (Xy0:a), (a->(((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))->((S Xp)->((Xp Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->((Xp Xx0) Xz))->(((S Xp)->((Xp Xy0) Xz))->P)))=> (((((and_rect ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((S Xp)->((Xp Xx0) Xz))) (x6:((S Xp)->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((S Xp)->((Xp Xx0) Xz))) ((S Xp)->((Xp Xy0) Xz)))->((S Xp)->((Xp Xx0) Xz)))))
% Found x401:=(x40 x400):((Xp Xx0) Xz)
% Found (x40 x400) as proof of ((Xp Xx0) Xz)
% Found ((x4 x30) x400) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)) as proof of ((Xp Xx0) Xz)
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->((Xp Xx0) Xz))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400))) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400))) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400))) as proof of ((Xp Xx0) Xz)
% Found (fun (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of ((Xp Xx0) Xz)
% Found (fun (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of ((S Xp)->((Xp Xx0) Xz))
% Found (fun (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) Xz)))
% Found (fun (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) Xz))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) Xz))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) Xz))))))
% Found x500:=(x50 x400):((Xp Xx) Xz0)
% Found (x50 x400) as proof of ((Xp Xx) Xz0)
% Found ((x5 x30) x400) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)) as proof of ((Xp Xx) Xz0)
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)) as proof of (((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->((Xp Xx) Xz0))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400))) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400))) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400))) as proof of ((Xp Xx) Xz0)
% Found (fun (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of ((Xp Xx) Xz0)
% Found (fun (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of ((S Xp)->((Xp Xx) Xz0))
% Found (fun (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xz0)))
% Found (fun (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx) Xz0))))))
% Found x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))
% Found (fun (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))
% Found (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5) as proof of ((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0))))))
% Found (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5) as proof of ((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))
% Found (and_rect20 (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5)) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))
% Found ((and_rect2 (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5)) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))
% Found (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5)) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))
% Found (fun (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5))) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))
% Found (fun (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5))) as proof of (((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5))) as proof of (forall (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xy0)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))=> x5))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp x50) Xy0)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp x50) Xz0))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp x50) Xz0))))))))
% Found x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))
% Found (fun (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))
% Found (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4) as proof of ((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400))))))
% Found (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4) as proof of ((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))))
% Found (and_rect20 (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4)) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))
% Found ((and_rect2 (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4)) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))
% Found (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4)) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))
% Found (fun (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4))) as proof of (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))
% Found (fun (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4))) as proof of (((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4))) as proof of (a->(((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400))))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400)))))))=> (((fun (P:Type) (x4:((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))->((S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400)))))) P) x4) x3)) (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400)))))) (fun (x4:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (x5:(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xy0) x400))))))=> x4))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->((Xp Xx0) x400)))))) (S (fun (x50:a) (x400:a)=> ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->((Xp Xy0) x400))))))->(S (fun (x50:a) (x400:a)=> ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->((Xp Xx0) x400))))))))
% Found x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))
% Found (fun (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))
% Found (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5) as proof of ((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500)))))
% Found (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5) as proof of ((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))))
% Found (and_rect20 (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5)) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))
% Found ((and_rect2 (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5)) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))
% Found (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5)) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))
% Found (fun (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5))) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))
% Found (fun (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5))) as proof of (((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5))) as proof of (a->(((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))=> x5))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xy0) x500)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp Xx0) x500)))))))
% Found x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))
% Found (fun (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))
% Found (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6) as proof of ((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))
% Found (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6) as proof of ((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))
% Found (and_rect20 (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6)) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))
% Found ((and_rect2 (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6)) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))
% Found (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6)) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))
% Found (fun (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6))) as proof of (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))
% Found (fun (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6))) as proof of (((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6))) as proof of (forall (Xz0:a), (((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))))=> (((fun (P:Type) (x5:((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))->((S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))->P)))=> (((((and_rect (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) P) x5) x4)) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0))))) (fun (x5:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (x6:(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xy0))))) (S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))->(S (fun (x60:a) (x500:a)=> ((S Xp)->((Xp x60) Xz0)))))))
% Found x6:(S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xx0))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xz0))))))
% Found x6:(S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xx0))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (S (fun (x70:a)=> (Xp Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xx0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xx0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a)=> (Xp Xx0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xx0))))))
% Found x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))))
% Found x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))))
% Found x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7) as proof of ((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))
% Found (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7) as proof of ((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found ((and_rect2 (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))))
% Found x6:(S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found ((and_rect2 (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))))
% Found x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found x6:(S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found ((and_rect2 (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7) as proof of ((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))
% Found (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7) as proof of ((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found ((and_rect2 (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x40:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x40:a)=> ((Xp x50) Xz0))))))
% Found x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7) as proof of ((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))
% Found (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7) as proof of ((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found ((and_rect2 (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7)) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (x5:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))->((S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))->P)))=> (((((and_rect (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) P) x6) x5)) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0)))) (fun (x6:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (x7:(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x50:a) (x400:a)=> ((Xp x50) Xy0)))) (S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))->(S (fun (x50:a) (x400:a)=> ((Xp x50) Xz0))))))
% Found x6:(S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6) as proof of ((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found ((and_rect2 (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x50:a)=> (Xp Xx0)))->((S (fun (x50:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x6:(S (fun (x50:a)=> (Xp Xx0)))) (x7:(S (fun (x50:a)=> (Xp Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x50:a)=> (Xp Xx0)))) (S (fun (x50:a)=> (Xp Xy0))))->(S (fun (x50:a)=> (Xp Xx0))))))
% Found x60:=(x6 x40):(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))
% Found (x6 x40) as proof of (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))
% Found (fun (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)) as proof of (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))
% Found (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)) as proof of (((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))
% Found (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)) as proof of (((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))
% Found (and_rect20 (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40))) as proof of (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))
% Found ((and_rect2 (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40))) as proof of (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))
% Found (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))) P) x5) x4)) (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40))) as proof of (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))
% Found (fun (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))) P) x5) x4)) (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)))) as proof of (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))
% Found (fun (x4:((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))) P) x5) x4)) (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)))) as proof of ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))
% Found (fun (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))) P) x5) x4)) (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)))) as proof of (((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))->((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))) P) x5) x4)) (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)))) as proof of (forall (Xz0:a), (((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))->((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))) P) x5) x4)) (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))->((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))->(((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0))))) P) x5) x4)) (S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))) (fun (x5:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) (x6:((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))=> (x6 x40)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xy0))))) ((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))->((S Xp)->(S (fun (x500:a) (x400:a)=> ((Xp x500) Xz0)))))))
% Found x50:=(x5 x40):(S (fun (x500:a)=> (Xp Xx0)))
% Found (x5 x40) as proof of (S (fun (x500:a)=> (Xp Xx0)))
% Found (fun (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)) as proof of (S (fun (x500:a)=> (Xp Xx0)))
% Found (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)) as proof of (((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->(S (fun (x500:a)=> (Xp Xx0))))
% Found (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)) as proof of (((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->(S (fun (x500:a)=> (Xp Xx0)))))
% Found (and_rect20 (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40))) as proof of (S (fun (x500:a)=> (Xp Xx0)))
% Found ((and_rect2 (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40))) as proof of (S (fun (x500:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))) P) x5) x4)) (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40))) as proof of (S (fun (x500:a)=> (Xp Xx0)))
% Found (fun (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))) P) x5) x4)) (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)))) as proof of (S (fun (x500:a)=> (Xp Xx0)))
% Found (fun (x4:((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))) P) x5) x4)) (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)))) as proof of ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))
% Found (fun (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))) P) x5) x4)) (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)))) as proof of (((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))->((S Xp)->(S (fun (x500:a)=> (Xp Xx0)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))) P) x5) x4)) (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)))) as proof of (a->(((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))->((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))) P) x5) x4)) (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)))) as proof of (forall (Xy0:a), (a->(((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))->((S Xp)->(S (fun (x500:a)=> (Xp Xx0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))) (x40:(S Xp))=> (((fun (P:Type) (x5:(((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))->(((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0))))) P) x5) x4)) (S (fun (x500:a)=> (Xp Xx0)))) (fun (x5:((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) (x6:((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))=> (x5 x40)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((S Xp)->(S (fun (x500:a)=> (Xp Xx0))))) ((S Xp)->(S (fun (x500:a)=> (Xp Xy0)))))->((S Xp)->(S (fun (x500:a)=> (Xp Xx0)))))))
% Found x1010:=(x101 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x101 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x10 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x10 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x3010:=(x301 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x301 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x30 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x30 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x30 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x30 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x30 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x30 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x1010:=(x101 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x101 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x10 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x10 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x401:=(x40 x400):(S (fun (x50:a)=> (Xp Xx0)))
% Found (x40 x400) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found ((x4 x30) x400) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (and_rect20 (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found ((and_rect2 (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)))) as proof of (S (fun (x50:a)=> (Xp Xx0)))
% Found (fun (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)))) as proof of ((S Xp)->(S (fun (x50:a)=> (Xp Xx0))))
% Found (fun (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))
% Found (fun (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0))))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0)))))) P) x4) x3)) (S (fun (x50:a)=> (Xp Xx0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))=> ((x4 x30) x400)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xy0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a)=> (Xp Xx0))))))))
% Found x500:=(x50 x400):(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found (x50 x400) as proof of (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found ((x5 x30) x400) as proof of (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found (fun (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)) as proof of (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)) as proof of (((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))
% Found (and_rect20 (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400))) as proof of (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found ((and_rect2 (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400))) as proof of (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400))) as proof of (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found (fun (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)))) as proof of (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))
% Found (fun (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)))) as proof of ((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))
% Found (fun (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))
% Found (fun (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))) (x30:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))) (x400:(S Xp))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))))) P) x4) x3)) (S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0)))) (fun (x4:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) (x5:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))=> ((x5 x30) x400)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xy0)))))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((S Xp)->(S (fun (x50:a) (x4000:a)=> ((Xp x50) Xz0))))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))))
% Found x1010:=(x101 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x101 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x10 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x10 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x10 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy00) Xy0)) ((Xp Xy0) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy0)) ((Xp Xy0) x600)))))))
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found ((and_rect2 ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))))
% Found x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found ((and_rect2 ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))))
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found ((and_rect2 ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))))
% Found x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7) as proof of (((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found ((and_rect2 ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7)) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))->(((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))->P)))=> (((((and_rect ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) P) x6) x5)) ((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))) (fun (x6:((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) (x7:((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))) (S (fun (x70:a)=> (Xp Xy0))))) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0)))))->((and (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))) (S (fun (x70:a)=> (Xp Xy0))))))))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) (x7:((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))) ((and (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy0)))->((S (fun (x70:a)=> (Xp Xy0)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy0)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy0)))) (x7:(S (fun (x70:a)=> (Xp Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy0)))) (S (fun (x70:a)=> (Xp Xy0))))->(S (fun (x70:a)=> (Xp Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x3010:=(x301 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a;Xy00:=Xx:a
% Found (fun (Xz0:a)=> x3010) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a;Xy00:=Xx:a
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a;Xy00:=Xx:a
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a;Xy00:=Xx:a
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x3010:=(x301 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x3010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x3010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x3010:=(x301 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x3010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x3010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x3010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy000))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))))
% Found x3010:=(x301 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x301 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x30 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x30 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x3010:=(x301 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x301 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x30 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x30 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x30 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a;Xy00:=Xx:a
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy0000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(a->(a->(((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))) ((and ((Xp Xy0) Xy00)) ((Xp Xy00) Xz)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz)))))
% Found x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx) Xy00)) ((Xp Xy00) Xz0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy0:=Xx:a;Xy00:=Xx:a
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy010) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy0))->((Xp Xx) Xy0))
% Instantiate: Xy00:=Xx:a
% Found x1010 as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xz0:a)=> x1010) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))
% Found (fun (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> x1010) as proof of (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x1010:=(x101 Xy00):(((and ((Xp Xx) Xy00)) ((Xp Xy00) Xy00))->((Xp Xx) Xy00))
% Found (x101 Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found ((x10 Xy00) Xy00) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))
% Found (fun (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a)=> ((x10 Xy00) Xy00)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy00)) ((Xp Xx) Xy00))->((Xp Xx) Xy00)))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy000))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy000) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy000) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xy000) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy000) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xy000) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy000) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xy000) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy000) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xy000) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy01))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xy0))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp x70) Xy00)) ((Xp Xy00) Xz0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))->((S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600))))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (x7:(S (fun (x70:a) (x600:a)=> ((and ((Xp Xy01) Xy00)) ((Xp Xy00) x600)))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600))))) (S (fun (x70:a) (x600:a)=> ((and ((Xp Xy0) Xy00)) ((Xp Xy00) x600)))))->(S (fun (x70:a) (x600:a)=> ((and ((Xp Xx0) Xy00)) ((Xp Xy00) x600)))))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy000) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xy000) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy000) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xy000) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy000) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy000) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy000)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy000)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy0000:a) (Xz0:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy0000:a) (Xz00:a), (((and ((Xp Xy00) Xy0000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy00) Xy000)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy0000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy0000:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0000) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy000) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz)
% Found (fun (x7:((Xp Xy00) Xz))=> x7) as proof of ((Xp Xy00) Xz)
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->((Xp Xy00) Xz))
% Found (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7) as proof of (((Xp Xy00) Xz)->(((Xp Xy00) Xz)->((Xp Xy00) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found ((and_rect2 ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7)) as proof of ((Xp Xy00) Xz)
% Found (fun (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of ((Xp Xy00) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xz)->(((Xp Xy00) Xz)->P)))=> (((((and_rect ((Xp Xy00) Xz)) ((Xp Xy00) Xz)) P) x6) x5)) ((Xp Xy00) Xz)) (fun (x6:((Xp Xy00) Xz)) (x7:((Xp Xy00) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy00) Xz)) ((Xp Xy00) Xz))->((Xp Xy00) Xz)))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx0) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx0) Xy00))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00)))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7) as proof of (((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (and_rect20 (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found ((and_rect2 ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7)) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))=> (((fun (P:Type) (x6:(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->P)))=> (((((and_rect ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) P) x6) x5)) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (fun (x6:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) (x7:((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))) ((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))->((and (a->(a->(a->(((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xy00) Xy0)))))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7) as proof of (((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (and_rect20 (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found ((and_rect2 ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7)) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))=> (((fun (P:Type) (x6:(((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))->(((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))->P)))=> (((((and_rect ((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) P) x6) x5)) ((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))) (fun (x6:((and (a->(forall (Xy010:a) (Xz0:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) (x7:((and (a->(forall (Xy010:a) (Xz00:a), (((and ((Xp Xy00) Xy010)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (a->(forall (Xy01:a) (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))) (S (fun (x70:a)=> (Xp Xy00))))) ((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00)))))->((and (a->(forall (Xy01:a) (Xz00:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz00))->((Xp Xy00) Xz00))))) (S (fun (x70:a)=> (Xp Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7) as proof of (((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (fun (x6:((and (forall (Xx00:a) (Xy010:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) (x7:((and (forall (Xx0:a) (Xy010:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy010) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))) ((and (forall (Xx0:a) (Xy01:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx0) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))->((and (forall (Xx00:a) (Xy01:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy000)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy000:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy000) Xy000))))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy01)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xy0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xy00) Xz0))))))
% Found x7:(S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7) as proof of ((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found ((and_rect2 (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7)) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (S (fun (x70:a)=> (Xp Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a)=> (Xp Xy00)))->((S (fun (x70:a)=> (Xp Xy00)))->P)))=> (((((and_rect (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00)))) P) x6) x5)) (S (fun (x70:a)=> (Xp Xy00)))) (fun (x6:(S (fun (x70:a)=> (Xp Xy00)))) (x7:(S (fun (x70:a)=> (Xp Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a)=> (Xp Xy00)))) (S (fun (x70:a)=> (Xp Xy00))))->(S (fun (x70:a)=> (Xp Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))=> x7))) as proof of (a->(a->(a->(((and (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp x70) Xy00)))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy01))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy0))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xx0))))))
% Found x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6) as proof of ((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (and_rect20 (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found ((and_rect2 (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6)) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found (fun (Xx0:a) (Xy01:a) (Xz0:a) (x5:((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))))=> (((fun (P:Type) (x6:((S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))->((S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))->P)))=> (((((and_rect (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00)))) P) x6) x5)) (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (fun (x6:(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (x7:(S (fun (x70:a) (x600:a)=> ((Xp Xy01) Xy00))))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00)))) (S (fun (x70:a) (x600:a)=> ((Xp Xy0) Xy00))))->(S (fun (x70:a) (x600:a)=> ((Xp Xx0) Xy00))))))
% Found x1010:=(x101 Xy01):(((and ((Xp Xx) Xy01)) ((Xp Xy01) Xy00))->((Xp Xx) Xy00))
% Instantiate: Xy01:=Xx:a;Xy00:=Xx:a
% Found (fun (Xz0:a)=> x1010
% EOF
%------------------------------------------------------------------------------