TSTP Solution File: SEV068^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV068^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n093.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 13:33:41 EDT 2014
% Result : Timeout 300.10s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV068^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n093.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 07:54:01 CDT 2014
% % CPUTime : 300.10
% 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 0x1a637e8>, <kernel.Type object at 0x1a63cb0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))), ((ex (a->(a->Prop))) (fun (Xp:(a->(a->Prop)))=> ((and ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (forall (Xq:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xq Xx) Xy))))))))) of role conjecture named cTHM275A_1_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))), ((ex (a->(a->Prop))) (fun (Xp:(a->(a->Prop)))=> ((and ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (forall (Xq:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xq Xx) Xy))))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))), ((ex (a->(a->Prop))) (fun (Xp:(a->(a->Prop)))=> ((and ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (forall (Xq:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xq Xx) Xy)))))))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))), ((ex (a->(a->Prop))) (fun (Xp:(a->(a->Prop)))=> ((and ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (forall (Xq:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xq Xx) Xy)))))))))
% Found x00:((x Xx) Xy)
% Instantiate: x:=Xq:(a->(a->Prop))
% Found x00 as proof of ((Xq Xx) Xy)
% Found (fun (x00:((x Xx) Xy))=> x00) as proof of ((Xq Xx) Xy)
% Found (fun (Xy:a) (x00:((x Xx) Xy))=> x00) as proof of (((x Xx) Xy)->((Xq Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x00:((x Xx) Xy))=> x00) as proof of (forall (Xy:a), (((x Xx) Xy)->((Xq Xx) Xy)))
% Found (fun (x0:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))) (Xx:a) (Xy:a) (x00:((x Xx) Xy))=> x00) as proof of (forall (Xx:a) (Xy:a), (((x Xx) Xy)->((Xq Xx) Xy)))
% Found x0000:=(x000 x0):((Xq Xx) Xy)
% Found (x000 x0) as proof of ((Xq Xx) Xy)
% Found ((x00 Xq) x0) as proof of ((Xq Xx) Xy)
% Found ((x00 Xq) x0) as proof of ((Xq Xx) Xy)
% Found (fun (x00:((x Xx) Xy))=> ((x00 Xq) x0)) as proof of ((Xq Xx) Xy)
% Found (fun (Xy:a) (x00:((x Xx) Xy))=> ((x00 Xq) x0)) as proof of (((x Xx) Xy)->((Xq Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x00:((x Xx) Xy))=> ((x00 Xq) x0)) as proof of (forall (Xy:a), (((x Xx) Xy)->((Xq Xx) Xy)))
% Found (fun (x0:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))) (Xx:a) (Xy:a) (x00:((x Xx) Xy))=> ((x00 Xq) x0)) as proof of (forall (Xx:a) (Xy:a), (((x Xx) Xy)->((Xq Xx) Xy)))
% Found (fun (Xq:(a->(a->Prop))) (x0:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))) (Xx:a) (Xy:a) (x00:((x Xx) Xy))=> ((x00 Xq) x0)) as proof of (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))->(forall (Xx:a) (Xy:a), (((x Xx) Xy)->((Xq Xx) Xy))))
% Found (fun (Xq:(a->(a->Prop))) (x0:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))) (Xx:a) (Xy:a) (x00:((x Xx) Xy))=> ((x00 Xq) x0)) as proof of (forall (Xq:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xq Xx) Xy)) ((Xq Xy) Xz))->((Xq Xx) Xz)))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xq Xx) Xy))))->(forall (Xx:a) (Xy:a), (((x Xx) Xy)->((Xq Xx) Xy)))))
% Found x0:((Xr Xx) Xy)
% Instantiate: x:=Xr:(a->(a->Prop))
% Found (fun (x0:((Xr Xx) Xy))=> x0) as proof of ((x Xx) Xy)
% Found (fun (Xy:a) (x0:((Xr Xx) Xy))=> x0) as proof of (((Xr Xx) Xy)->((x Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x0:((Xr Xx) Xy))=> x0) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((x Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x0:((Xr Xx) Xy))=> x0) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((x Xx) Xy)))
% Found x2000:=(x200 x0):((Xq Xx) Xy)
% Found (x200 x0) as proof of ((Xq Xx) Xy)
% Found ((x20 Xy) x0) as proof of ((Xq Xx) Xy)
% Found (((x2 Xx) Xy) x0) as proof of ((Xq Xx) Xy)
% Found (fun (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)) as proof of ((Xq Xx) Xy)
% Found (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->((Xq Xx) Xy))
% Found (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->((Xq Xx) Xy)))
% Found (and_rect00 (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0))) as proof of ((Xq Xx) Xy)
% Found ((and_rect0 ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0))) as proof of ((Xq Xx) Xy)
% Found (((fun (P:Type) (x1:((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))) P) x1) x00)) ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0))) as proof of ((Xq Xx) Xy)
% Found (fun (x00:((and (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))))=> (((fun (P:Type) (x1:((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))) P) x1) x00)) ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)))) as proof of ((Xq Xx) Xy)
% Found (fun (Xq:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))))=> (((fun (P:Type) (x1:((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))) P) x1) x00)) ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)))) as proof of (((and (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))->((Xq Xx) Xy))
% Found (fun (x0:((Xr Xx) Xy)) (Xq:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))))=> (((fun (P:Type) (x1:((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))) P) x1) x00)) ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)))) as proof of ((x Xx) Xy)
% Found (fun (Xy:a) (x0:((Xr Xx) Xy)) (Xq:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))))=> (((fun (P:Type) (x1:((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))) P) x1) x00)) ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)))) as proof of (((Xr Xx) Xy)->((x Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x0:((Xr Xx) Xy)) (Xq:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))))=> (((fun (P:Type) (x1:((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))) P) x1) x00)) ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)))) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((x Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x0:((Xr Xx) Xy)) (Xq:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))))=> (((fun (P:Type) (x1:((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0)))) P) x1) x00)) ((Xq Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))) (x2:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xy0))))=> (((x2 Xx) Xy) x0)))) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((x Xx) Xy)))
% Found x03:((x Xx0) Xz)
% Found (fun (x04:((x Xy0) Xz))=> x03) as proof of ((x Xx0) Xz)
% Found (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03) as proof of (((x Xy0) Xz)->((x Xx0) Xz))
% Found (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03) as proof of (((x Xx0) Xz)->(((x Xy0) Xz)->((x Xx0) Xz)))
% Found (and_rect10 (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03)) as proof of ((x Xx0) Xz)
% Found ((and_rect1 ((x Xx0) Xz)) (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03)) as proof of ((x Xx0) Xz)
% Found (((fun (P:Type) (x1:(((x Xx0) Xz)->(((x Xy0) Xz)->P)))=> (((((and_rect ((x Xx0) Xz)) ((x Xy0) Xz)) P) x1) x02)) ((x Xx0) Xz)) (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03)) as proof of ((x Xx0) Xz)
% Found (fun (x02:((and ((x Xx0) Xz)) ((x Xy0) Xz)))=> (((fun (P:Type) (x1:(((x Xx0) Xz)->(((x Xy0) Xz)->P)))=> (((((and_rect ((x Xx0) Xz)) ((x Xy0) Xz)) P) x1) x02)) ((x Xx0) Xz)) (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03))) as proof of ((x Xx0) Xz)
% Found (fun (Xz0:a) (x02:((and ((x Xx0) Xz)) ((x Xy0) Xz)))=> (((fun (P:Type) (x1:(((x Xx0) Xz)->(((x Xy0) Xz)->P)))=> (((((and_rect ((x Xx0) Xz)) ((x Xy0) Xz)) P) x1) x02)) ((x Xx0) Xz)) (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03))) as proof of (((and ((x Xx0) Xz)) ((x Xy0) Xz))->((x Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and ((x Xx0) Xz)) ((x Xy0) Xz)))=> (((fun (P:Type) (x1:(((x Xx0) Xz)->(((x Xy0) Xz)->P)))=> (((((and_rect ((x Xx0) Xz)) ((x Xy0) Xz)) P) x1) x02)) ((x Xx0) Xz)) (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03))) as proof of (a->(((and ((x Xx0) Xz)) ((x Xy0) Xz))->((x Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and ((x Xx0) Xz)) ((x Xy0) Xz)))=> (((fun (P:Type) (x1:(((x Xx0) Xz)->(((x Xy0) Xz)->P)))=> (((((and_rect ((x Xx0) Xz)) ((x Xy0) Xz)) P) x1) x02)) ((x Xx0) Xz)) (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03))) as proof of (forall (Xy0:a), (a->(((and ((x Xx0) Xz)) ((x Xy0) Xz))->((x Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and ((x Xx0) Xz)) ((x Xy0) Xz)))=> (((fun (P:Type) (x1:(((x Xx0) Xz)->(((x Xy0) Xz)->P)))=> (((((and_rect ((x Xx0) Xz)) ((x Xy0) Xz)) P) x1) x02)) ((x Xx0) Xz)) (fun (x03:((x Xx0) Xz)) (x04:((x Xy0) Xz))=> x03))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((x Xx0) Xz)) ((x Xy0) Xz))->((x Xx0) Xz))))
% Found x04:((x Xx) Xz0)
% Found (fun (x04:((x Xx) Xz0))=> x04) as proof of ((x Xx) Xz0)
% Found (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04) as proof of (((x Xx) Xz0)->((x Xx) Xz0))
% Found (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04) as proof of (((x Xx) Xy0)->(((x Xx) Xz0)->((x Xx) Xz0)))
% Found (and_rect10 (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04)) as proof of ((x Xx) Xz0)
% Found ((and_rect1 ((x Xx) Xz0)) (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04)) as proof of ((x Xx) Xz0)
% Found (((fun (P:Type) (x1:(((x Xx) Xy0)->(((x Xx) Xz0)->P)))=> (((((and_rect ((x Xx) Xy0)) ((x Xx) Xz0)) P) x1) x02)) ((x Xx) Xz0)) (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04)) as proof of ((x Xx) Xz0)
% Found (fun (x02:((and ((x Xx) Xy0)) ((x Xx) Xz0)))=> (((fun (P:Type) (x1:(((x Xx) Xy0)->(((x Xx) Xz0)->P)))=> (((((and_rect ((x Xx) Xy0)) ((x Xx) Xz0)) P) x1) x02)) ((x Xx) Xz0)) (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04))) as proof of ((x Xx) Xz0)
% Found (fun (Xz0:a) (x02:((and ((x Xx) Xy0)) ((x Xx) Xz0)))=> (((fun (P:Type) (x1:(((x Xx) Xy0)->(((x Xx) Xz0)->P)))=> (((((and_rect ((x Xx) Xy0)) ((x Xx) Xz0)) P) x1) x02)) ((x Xx) Xz0)) (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04))) as proof of (((and ((x Xx) Xy0)) ((x Xx) Xz0))->((x Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and ((x Xx) Xy0)) ((x Xx) Xz0)))=> (((fun (P:Type) (x1:(((x Xx) Xy0)->(((x Xx) Xz0)->P)))=> (((((and_rect ((x Xx) Xy0)) ((x Xx) Xz0)) P) x1) x02)) ((x Xx) Xz0)) (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04))) as proof of (forall (Xz0:a), (((and ((x Xx) Xy0)) ((x Xx) Xz0))->((x Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and ((x Xx) Xy0)) ((x Xx) Xz0)))=> (((fun (P:Type) (x1:(((x Xx) Xy0)->(((x Xx) Xz0)->P)))=> (((((and_rect ((x Xx) Xy0)) ((x Xx) Xz0)) P) x1) x02)) ((x Xx) Xz0)) (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((x Xx) Xy0)) ((x Xx) Xz0))->((x Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and ((x Xx) Xy0)) ((x Xx) Xz0)))=> (((fun (P:Type) (x1:(((x Xx) Xy0)->(((x Xx) Xz0)->P)))=> (((((and_rect ((x Xx) Xy0)) ((x Xx) Xz0)) P) x1) x02)) ((x Xx) Xz0)) (fun (x03:((x Xx) Xy0)) (x04:((x Xx) Xz0))=> x04))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((x Xx) Xy0)) ((x Xx) Xz0))->((x Xx) Xz0))))
% Found x1:((Xq Xx0) Xz)
% Found (fun (x2:((Xq Xy0) Xz))=> x1) as proof of ((Xq Xx0) Xz)
% Found (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1) as proof of (((Xq Xy0) Xz)->((Xq Xx0) Xz))
% Found (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1) as proof of (((Xq Xx0) Xz)->(((Xq Xy0) Xz)->((Xq Xx0) Xz)))
% Found (and_rect10 (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1)) as proof of ((Xq Xx0) Xz)
% Found ((and_rect1 ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1)) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1)) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of ((Xq Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (forall (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found x2:((Xq Xx) Xz0)
% Found (fun (x2:((Xq Xx) Xz0))=> x2) as proof of ((Xq Xx) Xz0)
% Found (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2) as proof of (((Xq Xx) Xz0)->((Xq Xx) Xz0))
% Found (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2) as proof of (((Xq Xx) Xy0)->(((Xq Xx) Xz0)->((Xq Xx) Xz0)))
% Found (and_rect10 (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2)) as proof of ((Xq Xx) Xz0)
% Found ((and_rect1 ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2)) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2)) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of ((Xq Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))))
% Found x1:((Xq Xx0) Xz)
% Found (fun (x2:((Xq Xy0) Xz))=> x1) as proof of ((Xq Xx0) Xz)
% Found (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1) as proof of (((Xq Xy0) Xz)->((Xq Xx0) Xz))
% Found (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1) as proof of (((Xq Xx0) Xz)->(((Xq Xy0) Xz)->((Xq Xx0) Xz)))
% Found (and_rect10 (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1)) as proof of ((Xq Xx0) Xz)
% Found ((and_rect1 ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1)) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1)) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of ((Xq Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (forall (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((Xq Xx0) Xz)) (x2:((Xq Xy0) Xz))=> x1))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found x2:((Xq Xx) Xz0)
% Found (fun (x2:((Xq Xx) Xz0))=> x2) as proof of ((Xq Xx) Xz0)
% Found (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2) as proof of (((Xq Xx) Xz0)->((Xq Xx) Xz0))
% Found (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2) as proof of (((Xq Xx) Xy0)->(((Xq Xx) Xz0)->((Xq Xx) Xz0)))
% Found (and_rect10 (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2)) as proof of ((Xq Xx) Xz0)
% Found ((and_rect1 ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2)) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2)) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of ((Xq Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((Xq Xx) Xy0)) (x2:((Xq Xx) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))))
% Found x20:=(x2 x020):((Xq Xx) Xz0)
% Found (x2 x020) as proof of ((Xq Xx) Xz0)
% Found (fun (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)) as proof of ((Xq Xx) Xz0)
% Found (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)) as proof of ((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)) as proof of ((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (and_rect10 (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020))) as proof of ((Xq Xx) Xz0)
% Found ((and_rect1 ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020))) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))) P) x1) x02)) ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020))) as proof of ((Xq Xx) Xz0)
% Found (fun (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))) P) x1) x02)) ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)))) as proof of ((Xq Xx) Xz0)
% Found (fun (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))) P) x1) x02)) ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)))) as proof of (((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx) Xz0))
% Found (fun (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))) P) x1) x02)) ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)))) as proof of (((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx) Xz0)))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))) P) x1) x02)) ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)))) as proof of (forall (Xz0:a), (((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))) P) x1) x02)) ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))->((((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0))) P) x1) x02)) ((Xq Xx) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (x2:(((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))=> (x2 x020)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx) Xy0))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xx) Xz0)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx) Xz0)))))
% Found x10:=(x1 x020):((Xq Xx0) Xz)
% Found (x1 x020) as proof of ((Xq Xx0) Xz)
% Found (fun (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)) as proof of ((Xq Xx0) Xz)
% Found (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)) as proof of ((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)) as proof of ((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (and_rect10 (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020))) as proof of ((Xq Xx0) Xz)
% Found ((and_rect1 ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020))) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))) P) x1) x02)) ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020))) as proof of ((Xq Xx0) Xz)
% Found (fun (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))) P) x1) x02)) ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)))) as proof of ((Xq Xx0) Xz)
% Found (fun (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))) P) x1) x02)) ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)))) as proof of (((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx0) Xz))
% Found (fun (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))) P) x1) x02)) ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)))) as proof of (((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx0) Xz)))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))) P) x1) x02)) ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)))) as proof of (a->(((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))) P) x1) x02)) ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)))) as proof of (forall (Xy0:a), (a->(((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))) (x020:((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))->((((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz))) P) x1) x02)) ((Xq Xx0) Xz)) (fun (x1:(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (x2:(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xy0) Xz)))=> (x1 x020)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz))) (((and (forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00))))->((Xq Xy0) Xz)))->(((and (forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))->((Xq Xx0) Xz)))))
% Found x3:((Xq Xx0) Xz)
% Found (fun (x4:((Xq Xy0) Xz))=> x3) as proof of ((Xq Xx0) Xz)
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xy0) Xz)->((Xq Xx0) Xz))
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xx0) Xz)->(((Xq Xy0) Xz)->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of ((Xq Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found x4:((Xq Xx) Xz0)
% Found (fun (x4:((Xq Xx) Xz0))=> x4) as proof of ((Xq Xx) Xz0)
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xz0)->((Xq Xx) Xz0))
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xy0)->(((Xq Xx) Xz0)->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of ((Xq Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))))
% Found x4:((Xq Xx) Xz0)
% Found (fun (x4:((Xq Xx) Xz0))=> x4) as proof of ((Xq Xx) Xz0)
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xz0)->((Xq Xx) Xz0))
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xy0)->(((Xq Xx) Xz0)->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of ((Xq Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))))
% Found x3:((Xq Xx0) Xz)
% Found (fun (x4:((Xq Xy0) Xz))=> x3) as proof of ((Xq Xx0) Xz)
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xy0) Xz)->((Xq Xx0) Xz))
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xx0) Xz)->(((Xq Xy0) Xz)->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of ((Xq Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found x4:((Xq Xx) Xz0)
% Found (fun (x4:((Xq Xx) Xz0))=> x4) as proof of ((Xq Xx) Xz0)
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xz0)->((Xq Xx) Xz0))
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xy0)->(((Xq Xx) Xz0)->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of ((Xq Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))))
% Found x3:((Xq Xx0) Xz)
% Found (fun (x4:((Xq Xy0) Xz))=> x3) as proof of ((Xq Xx0) Xz)
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xy0) Xz)->((Xq Xx0) Xz))
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xx0) Xz)->(((Xq Xy0) Xz)->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of ((Xq Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found x4:((Xq Xx) Xz0)
% Found (fun (x4:((Xq Xx) Xz0))=> x4) as proof of ((Xq Xx) Xz0)
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xz0)->((Xq Xx) Xz0))
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xy0)->(((Xq Xx) Xz0)->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of ((Xq Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))))
% Found x3:((Xq Xx0) Xz)
% Found (fun (x4:((Xq Xy0) Xz))=> x3) as proof of ((Xq Xx0) Xz)
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xy0) Xz)->((Xq Xx0) Xz))
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xx0) Xz)->(((Xq Xy0) Xz)->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of ((Xq Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found x4:((Xq Xx) Xz0)
% Found (fun (x4:((Xq Xx) Xz0))=> x4) as proof of ((Xq Xx) Xz0)
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xz0)->((Xq Xx) Xz0))
% Found (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4) as proof of (((Xq Xx) Xy0)->(((Xq Xx) Xz0)->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4)) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of ((Xq Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx) Xy0)->(((Xq Xx) Xz0)->P)))=> (((((and_rect ((Xq Xx) Xy0)) ((Xq Xx) Xz0)) P) x3) x03)) ((Xq Xx) Xz0)) (fun (x3:((Xq Xx) Xy0)) (x4:((Xq Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx) Xy0)) ((Xq Xx) Xz0))->((Xq Xx) Xz0))))
% Found x3:((Xq Xx0) Xz)
% Found (fun (x4:((Xq Xy0) Xz))=> x3) as proof of ((Xq Xx0) Xz)
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xy0) Xz)->((Xq Xx0) Xz))
% Found (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3) as proof of (((Xq Xx0) Xz)->(((Xq Xy0) Xz)->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3)) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of ((Xq Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xz)->(((Xq Xy0) Xz)->P)))=> (((((and_rect ((Xq Xx0) Xz)) ((Xq Xy0) Xz)) P) x3) x03)) ((Xq Xx0) Xz)) (fun (x3:((Xq Xx0) Xz)) (x4:((Xq Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xq Xx0) Xz)) ((Xq Xy0) Xz))->((Xq Xx0) Xz))))
% Found x30:=(x3 x200):((Xq Xx) Xz0)
% Found (x3 x200) as proof of ((Xq Xx) Xz0)
% Found (fun (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)) as proof of ((Xq Xx) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)) as proof of (((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200))) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200))) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200))) as proof of ((Xq Xx) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))))
% Found x20:=(x2 x200):((Xq Xx0) Xz)
% Found (x2 x200) as proof of ((Xq Xx0) Xz)
% Found (fun (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)) as proof of ((Xq Xx0) Xz)
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200))) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200))) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200))) as proof of ((Xq Xx0) Xz)
% Found (fun (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))))
% Found x04:((x Xx00) Xy0)
% Found (fun (x05:((x Xy00) Xy0))=> x04) as proof of ((x Xx00) Xy0)
% Found (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04) as proof of (((x Xy00) Xy0)->((x Xx00) Xy0))
% Found (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04) as proof of (((x Xx00) Xy0)->(((x Xy00) Xy0)->((x Xx00) Xy0)))
% Found (and_rect10 (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04)) as proof of ((x Xx00) Xy0)
% Found ((and_rect1 ((x Xx00) Xy0)) (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04)) as proof of ((x Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((x Xx00) Xy0)->(((x Xy00) Xy0)->P)))=> (((((and_rect ((x Xx00) Xy0)) ((x Xy00) Xy0)) P) x1) x03)) ((x Xx00) Xy0)) (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04)) as proof of ((x Xx00) Xy0)
% Found (fun (x03:((and ((x Xx00) Xy0)) ((x Xy00) Xy0)))=> (((fun (P:Type) (x1:(((x Xx00) Xy0)->(((x Xy00) Xy0)->P)))=> (((((and_rect ((x Xx00) Xy0)) ((x Xy00) Xy0)) P) x1) x03)) ((x Xx00) Xy0)) (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04))) as proof of ((x Xx00) Xy0)
% Found (fun (Xz0:a) (x03:((and ((x Xx00) Xy0)) ((x Xy00) Xy0)))=> (((fun (P:Type) (x1:(((x Xx00) Xy0)->(((x Xy00) Xy0)->P)))=> (((((and_rect ((x Xx00) Xy0)) ((x Xy00) Xy0)) P) x1) x03)) ((x Xx00) Xy0)) (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04))) as proof of (((and ((x Xx00) Xy0)) ((x Xy00) Xy0))->((x Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((x Xx00) Xy0)) ((x Xy00) Xy0)))=> (((fun (P:Type) (x1:(((x Xx00) Xy0)->(((x Xy00) Xy0)->P)))=> (((((and_rect ((x Xx00) Xy0)) ((x Xy00) Xy0)) P) x1) x03)) ((x Xx00) Xy0)) (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04))) as proof of (a->(((and ((x Xx00) Xy0)) ((x Xy00) Xy0))->((x Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((x Xx00) Xy0)) ((x Xy00) Xy0)))=> (((fun (P:Type) (x1:(((x Xx00) Xy0)->(((x Xy00) Xy0)->P)))=> (((((and_rect ((x Xx00) Xy0)) ((x Xy00) Xy0)) P) x1) x03)) ((x Xx00) Xy0)) (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04))) as proof of (forall (Xy00:a), (a->(((and ((x Xx00) Xy0)) ((x Xy00) Xy0))->((x Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((x Xx00) Xy0)) ((x Xy00) Xy0)))=> (((fun (P:Type) (x1:(((x Xx00) Xy0)->(((x Xy00) Xy0)->P)))=> (((((and_rect ((x Xx00) Xy0)) ((x Xy00) Xy0)) P) x1) x03)) ((x Xx00) Xy0)) (fun (x04:((x Xx00) Xy0)) (x05:((x Xy00) Xy0))=> x04))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((x Xx0) Xy0)) ((x Xy00) Xy0))->((x Xx0) Xy0))))
% Found x05:((x Xx0) Xz0)
% Found (fun (x05:((x Xx0) Xz0))=> x05) as proof of ((x Xx0) Xz0)
% Found (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05) as proof of (((x Xx0) Xz0)->((x Xx0) Xz0))
% Found (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05) as proof of (((x Xx0) Xy00)->(((x Xx0) Xz0)->((x Xx0) Xz0)))
% Found (and_rect10 (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05)) as proof of ((x Xx0) Xz0)
% Found ((and_rect1 ((x Xx0) Xz0)) (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05)) as proof of ((x Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((x Xx0) Xy00)->(((x Xx0) Xz0)->P)))=> (((((and_rect ((x Xx0) Xy00)) ((x Xx0) Xz0)) P) x1) x03)) ((x Xx0) Xz0)) (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05)) as proof of ((x Xx0) Xz0)
% Found (fun (x03:((and ((x Xx0) Xy00)) ((x Xx0) Xz0)))=> (((fun (P:Type) (x1:(((x Xx0) Xy00)->(((x Xx0) Xz0)->P)))=> (((((and_rect ((x Xx0) Xy00)) ((x Xx0) Xz0)) P) x1) x03)) ((x Xx0) Xz0)) (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05))) as proof of ((x Xx0) Xz0)
% Found (fun (Xz0:a) (x03:((and ((x Xx0) Xy00)) ((x Xx0) Xz0)))=> (((fun (P:Type) (x1:(((x Xx0) Xy00)->(((x Xx0) Xz0)->P)))=> (((((and_rect ((x Xx0) Xy00)) ((x Xx0) Xz0)) P) x1) x03)) ((x Xx0) Xz0)) (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05))) as proof of (((and ((x Xx0) Xy00)) ((x Xx0) Xz0))->((x Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((x Xx0) Xy00)) ((x Xx0) Xz0)))=> (((fun (P:Type) (x1:(((x Xx0) Xy00)->(((x Xx0) Xz0)->P)))=> (((((and_rect ((x Xx0) Xy00)) ((x Xx0) Xz0)) P) x1) x03)) ((x Xx0) Xz0)) (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05))) as proof of (forall (Xz0:a), (((and ((x Xx0) Xy00)) ((x Xx0) Xz0))->((x Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((x Xx0) Xy00)) ((x Xx0) Xz0)))=> (((fun (P:Type) (x1:(((x Xx0) Xy00)->(((x Xx0) Xz0)->P)))=> (((((and_rect ((x Xx0) Xy00)) ((x Xx0) Xz0)) P) x1) x03)) ((x Xx0) Xz0)) (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((x Xx0) Xy0)) ((x Xx0) Xz0))->((x Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((x Xx0) Xy00)) ((x Xx0) Xz0)))=> (((fun (P:Type) (x1:(((x Xx0) Xy00)->(((x Xx0) Xz0)->P)))=> (((((and_rect ((x Xx0) Xy00)) ((x Xx0) Xz0)) P) x1) x03)) ((x Xx0) Xz0)) (fun (x04:((x Xx0) Xy00)) (x05:((x Xx0) Xz0))=> x05))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((x Xx0) Xy0)) ((x Xx0) Xz0))->((x Xx0) Xz0))))
% Found x20:=(x2 x200):((Xq Xx0) Xz)
% Found (x2 x200) as proof of ((Xq Xx0) Xz)
% Found (fun (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)) as proof of ((Xq Xx0) Xz)
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->((Xq Xx0) Xz))
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200))) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200))) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200))) as proof of ((Xq Xx0) Xz)
% Found (fun (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of ((Xq Xx0) Xz)
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))) P) x2) x03)) ((Xq Xx0) Xz)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) (x3:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))))
% Found x30:=(x3 x200):((Xq Xx) Xz0)
% Found (x3 x200) as proof of ((Xq Xx) Xz0)
% Found (fun (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)) as proof of ((Xq Xx) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)) as proof of (((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->((Xq Xx) Xz0))
% Found (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200))) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200))) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200))) as proof of ((Xq Xx) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx) Xz0)
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) (x200:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))) P) x2) x03)) ((Xq Xx) Xz0)) (fun (x2:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) (x3:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))))
% Found x4:((Xr Xx) Xz0)
% Found (fun (x4:((Xr Xx) Xz0))=> x4) as proof of ((Xr Xx) Xz0)
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xz0)->((Xr Xx) Xz0))
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xz0)->((Xr Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found ((and_rect2 ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (fun (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of ((Xr Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))))
% Found x3:((Xr Xx0) Xz)
% Found (fun (x4:((Xr Xy0) Xz))=> x3) as proof of ((Xr Xx0) Xz)
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xy0) Xz)->((Xr Xx0) Xz))
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xx0) Xz)->(((Xr Xy0) Xz)->((Xr Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found ((and_rect2 ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (fun (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of ((Xr Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found x101:=(x10 x20):((Xq Xx0) Xz)
% Found (x10 x20) as proof of ((Xq Xx0) Xz)
% Found ((x1 x100) x20) as proof of ((Xq Xx0) Xz)
% Found (fun (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)) as proof of ((Xq Xx0) Xz)
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->((Xq Xx0) Xz))
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20))) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20))) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20))) as proof of ((Xq Xx0) Xz)
% Found (fun (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of ((Xq Xx0) Xz)
% Found (fun (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))))
% Found x210:=(x21 x20):((Xq Xx) Xz0)
% Found (x21 x20) as proof of ((Xq Xx) Xz0)
% Found ((x2 x100) x20) as proof of ((Xq Xx) Xz0)
% Found (fun (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)) as proof of ((Xq Xx) Xz0)
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((Xq Xx) Xz0))
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx) Xz0)
% Found (fun (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of ((Xq Xx) Xz0)
% Found (fun (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))))
% Found x1:((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xy00) Xy0))=> x1) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x2:((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xz0))=> x2) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x1:((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xy00) Xy0))=> x1) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x1:((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xy00) Xy0))=> x1) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x2:((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xz0))=> x2) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x2:((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xz0))=> x2) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x1:((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xy00) Xy0))=> x1) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x2:((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xz0))=> x2) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xr Xx0) Xz)
% Found (fun (x4:((Xr Xy0) Xz))=> x3) as proof of ((Xr Xx0) Xz)
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xy0) Xz)->((Xr Xx0) Xz))
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xx0) Xz)->(((Xr Xy0) Xz)->((Xr Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found ((and_rect2 ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (fun (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of ((Xr Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found x4:((Xr Xx) Xz0)
% Found (fun (x4:((Xr Xx) Xz0))=> x4) as proof of ((Xr Xx) Xz0)
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xz0)->((Xr Xx) Xz0))
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xz0)->((Xr Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found ((and_rect2 ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (fun (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of ((Xr Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))))
% Found x4:((Xr Xx) Xz0)
% Found (fun (x4:((Xr Xx) Xz0))=> x4) as proof of ((Xr Xx) Xz0)
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xz0)->((Xr Xx) Xz0))
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xz0)->((Xr Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found ((and_rect2 ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (fun (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of ((Xr Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))))
% Found x3:((Xr Xx0) Xz)
% Found (fun (x4:((Xr Xy0) Xz))=> x3) as proof of ((Xr Xx0) Xz)
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xy0) Xz)->((Xr Xx0) Xz))
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xx0) Xz)->(((Xr Xy0) Xz)->((Xr Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found ((and_rect2 ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (fun (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of ((Xr Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found x040:=(x04 x020):((x Xx0) Xz0)
% Found (x04 x020) as proof of ((x Xx0) Xz0)
% Found (fun (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)) as proof of ((x Xx0) Xz0)
% Found (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)) as proof of ((((Xr Xx0) Xy0)->((x Xx0) Xz0))->((x Xx0) Xz0))
% Found (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)) as proof of ((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->((x Xx0) Xz0)))
% Found (and_rect10 (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020))) as proof of ((x Xx0) Xz0)
% Found ((and_rect1 ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020))) as proof of ((x Xx0) Xz0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020))) as proof of ((x Xx0) Xz0)
% Found (fun (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)))) as proof of ((x Xx0) Xz0)
% Found (fun (x02:((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)))) as proof of (((Xr Xx0) Xy0)->((x Xx0) Xz0))
% Found (fun (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)))) as proof of (((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))->(((Xr Xx0) Xy0)->((x Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))->(((Xr Xx0) Xy0)->((x Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))->(((Xr Xx0) Xy0)->((x Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx0) Xy00))->((((Xr Xx0) Xy0)->((x Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx0) Xy00))) (x04:(((Xr Xx0) Xy0)->((x Xx0) Xz0)))=> (x04 x020)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((x Xx0) Xy00))) (((Xr Xx0) Xy0)->((x Xx0) Xz0)))->(((Xr Xx0) Xy0)->((x Xx0) Xz0)))))
% Found x030:=(x03 x020):((x Xx00) Xy0)
% Found (x03 x020) as proof of ((x Xx00) Xy0)
% Found (fun (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)) as proof of ((x Xx00) Xy0)
% Found (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)) as proof of ((((Xr Xx0) Xy0)->((x Xy00) Xy0))->((x Xx00) Xy0))
% Found (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)) as proof of ((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->((x Xx00) Xy0)))
% Found (and_rect10 (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020))) as proof of ((x Xx00) Xy0)
% Found ((and_rect1 ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020))) as proof of ((x Xx00) Xy0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0))) P) x1) x02)) ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020))) as proof of ((x Xx00) Xy0)
% Found (fun (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0))) P) x1) x02)) ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)))) as proof of ((x Xx00) Xy0)
% Found (fun (x02:((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0))) P) x1) x02)) ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)))) as proof of (((Xr Xx0) Xy0)->((x Xx00) Xy0))
% Found (fun (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0))) P) x1) x02)) ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)))) as proof of (((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))->(((Xr Xx0) Xy0)->((x Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0))) P) x1) x02)) ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))->(((Xr Xx0) Xy0)->((x Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0))) P) x1) x02)) ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))->(((Xr Xx0) Xy0)->((x Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))) (x020:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((x Xx00) Xy0))->((((Xr Xx0) Xy0)->((x Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0))) P) x1) x02)) ((x Xx00) Xy0)) (fun (x03:(((Xr Xx0) Xy0)->((x Xx00) Xy0))) (x04:(((Xr Xx0) Xy0)->((x Xy00) Xy0)))=> (x03 x020)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((x Xx00) Xy0))) (((Xr Xx0) Xy0)->((x Xy00) Xy0)))->(((Xr Xx0) Xy0)->((x Xx00) Xy0)))))
% Found x4:((Xr Xx) Xz0)
% Found (fun (x4:((Xr Xx) Xz0))=> x4) as proof of ((Xr Xx) Xz0)
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xz0)->((Xr Xx) Xz0))
% Found (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xz0)->((Xr Xx) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found ((and_rect2 ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4)) as proof of ((Xr Xx) Xz0)
% Found (fun (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of ((Xr Xx) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x3) x03)) ((Xr Xx) Xz0)) (fun (x3:((Xr Xx) Xy0)) (x4:((Xr Xx) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))))
% Found x3:((Xr Xx0) Xz)
% Found (fun (x4:((Xr Xy0) Xz))=> x3) as proof of ((Xr Xx0) Xz)
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xy0) Xz)->((Xr Xx0) Xz))
% Found (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3) as proof of (((Xr Xx0) Xz)->(((Xr Xy0) Xz)->((Xr Xx0) Xz)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found ((and_rect2 ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3)) as proof of ((Xr Xx0) Xz)
% Found (fun (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of ((Xr Xx0) Xz)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x3) x03)) ((Xr Xx0) Xz)) (fun (x3:((Xr Xx0) Xz)) (x4:((Xr Xy0) Xz))=> x3))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found x210:=(x21 x20):((Xq Xx) Xz0)
% Found (x21 x20) as proof of ((Xq Xx) Xz0)
% Found ((x2 x100) x20) as proof of ((Xq Xx) Xz0)
% Found (fun (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)) as proof of ((Xq Xx) Xz0)
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((Xq Xx) Xz0))
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->((Xq Xx) Xz0)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx) Xz0)
% Found ((and_rect2 ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx) Xz0)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx) Xz0)
% Found (fun (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of ((Xq Xx) Xz0)
% Found (fun (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0)))) P) x1) x03)) ((Xq Xx) Xz0)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) (x2:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))=> ((x2 x100) x20)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xx) Xz0))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx) Xz0))))))
% Found x101:=(x10 x20):((Xq Xx0) Xz)
% Found (x10 x20) as proof of ((Xq Xx0) Xz)
% Found ((x1 x100) x20) as proof of ((Xq Xx0) Xz)
% Found (fun (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)) as proof of ((Xq Xx0) Xz)
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->((Xq Xx0) Xz))
% Found (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->((Xq Xx0) Xz)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20))) as proof of ((Xq Xx0) Xz)
% Found ((and_rect2 ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20))) as proof of ((Xq Xx0) Xz)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20))) as proof of ((Xq Xx0) Xz)
% Found (fun (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of ((Xq Xx0) Xz)
% Found (fun (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))
% Found (fun (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))) (x100:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz)))) P) x1) x03)) ((Xq Xx0) Xz)) (fun (x1:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) (x2:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xy0) Xz))))=> ((x1 x100) x20)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx0) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx0) Xz00)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy00)))->((Xq Xy0) Xz))))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xq Xx00) Xy0)) ((Xq Xy0) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xy0)))->((Xq Xx0) Xz))))))
% Found x20:=(x2 x020):((Xq Xx0) Xz0)
% Found (x2 x020) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)) as proof of ((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)) as proof of ((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x020:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) (x020:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)))) as proof of (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) (x020:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)))) as proof of (((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) (x020:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)))) as proof of (forall (Xz0:a), (((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) (x020:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xy0))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) (x020:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))->((((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))=> (x2 x020)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xy0))) (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))))
% Found x10:=(x1 x020):((Xq Xx00) Xy0)
% Found (x1 x020) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)) as proof of ((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)) as proof of ((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x020:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) (x020:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)))) as proof of (((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) (x020:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)))) as proof of (((and (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->(((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) (x020:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)))) as proof of (a->(((and (((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) (x020:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)))) as proof of (forall (Xy00:a), (a->(((and (((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) (x020:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))=> (x1 x020)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))) (((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0)))->(((and (forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xy0)))))
% Found x10:=(x1 x030):((Xq Xx00) Xy0)
% Found (x1 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))) (x030:((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))) (x030:((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (((and (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))->(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))) (x030:((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (a->(((and (((and (forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))->(((and (forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))) (x030:((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (forall (Xy00:a), (a->(((and (((and (forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))->(((and (forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))) (x030:((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))->((((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xx00) Xy0))) (x2:(((and (forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (((and (forall (Xx00:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx00) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))->((Xq Xx0) Xy0))) (((and (forall (Xx00:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx00) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))->((Xq Xy00) Xy0)))->(((and (forall (Xx00:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx00) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))->((Xq Xx0) Xy0)))))
% Found x20:=(x2 x030):((Xq Xx0) Xz0)
% Found (x2 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x10:=(x1 x030):((Xq Xx00) Xy0)
% Found (x1 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x20:=(x2 x030):((Xq Xx0) Xz0)
% Found (x2 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))) (x030:((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))) (x030:((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))->(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))) (x030:((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (forall (Xz0:a), (((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))->(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))) (x030:((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy0))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))->(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))) (x030:((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))))=> (((fun (P:Type) (x1:((((and (forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))->((((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xy00))) (x2:(((and (forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (((and (forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx1) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx1) Xz0)))) (forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1))))->((Xq Xx0) Xy0))) (((and (forall (Xx1:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx1) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx1) Xz00)))) (forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1))))->((Xq Xx0) Xz0)))->(((and (forall (Xx1:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx1) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx1) Xz00)))) (forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1))))->((Xq Xx0) Xz0)))))
% Found x20:=(x2 x030):((Xq Xx0) Xz0)
% Found (x2 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x2:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x2 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x10:=(x1 x030):((Xq Xx00) Xy0)
% Found (x1 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x2:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x1 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x0300:=(x030 x020):((x Xx00) Xy00)
% Found (x030 x020) as proof of ((x Xx00) Xy00)
% Found ((x03 Xy00) x020) as proof of ((x Xx00) Xy00)
% Found (fun (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)) as proof of ((x Xx00) Xy00)
% Found (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000)))->((x Xx00) Xy00))
% Found (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000)))->((x Xx00) Xy00)))
% Found (and_rect10 (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020))) as proof of ((x Xx00) Xy00)
% Found ((and_rect1 ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020))) as proof of ((x Xx00) Xy00)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020))) as proof of ((x Xx00) Xy00)
% Found (fun (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)))) as proof of ((x Xx00) Xy00)
% Found (fun (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)))) as proof of (((Xr Xx0) Xy00)->((x Xx00) Xy00))
% Found (fun (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx00) Xy0)))
% Found (fun (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx00) Xy00)) (fun (x03:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xx00) Xy000)))) (x04:(forall (Xy000:a), (((Xr Xx0) Xy000)->((x Xy0) Xy000))))=> ((x03 Xy00) x020)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx00) Xy0))))))
% Found x100:=(x10 x030):((Xq Xx00) Xy00)
% Found (x10 x030) as proof of ((Xq Xx00) Xy00)
% Found ((x1 Xy00) x030) as proof of ((Xq Xx00) Xy00)
% Found (fun (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)) as proof of ((Xq Xx00) Xy00)
% Found (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00))
% Found (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00)))
% Found (and_rect10 (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found ((and_rect1 ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (fun (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of ((Xq Xx00) Xy00)
% Found (fun (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (((Xr Xx0) Xy00)->((Xq Xx00) Xy00))
% Found (fun (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found x200:=(x20 x0200):((Xq Xx0) Xz0)
% Found (x20 x0200) as proof of ((Xq Xx0) Xz0)
% Found ((x2 x020) x0200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)) as proof of ((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0))
% Found (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)) as proof of ((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x0200:((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)))) as proof of (((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0))
% Found (fun (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))
% Found (fun (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)))) as proof of (((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))=> ((x2 x020) x0200)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0))))))
% Found x100:=(x10 x0200):((Xq Xx00) Xy0)
% Found (x10 x0200) as proof of ((Xq Xx00) Xy0)
% Found ((x1 x020) x0200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)) as proof of ((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0))
% Found (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)) as proof of ((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0)))
% Found (and_rect10 (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect1 ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x0200:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)))) as proof of (((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))
% Found (fun (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)))) as proof of (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)))) as proof of (((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)))) as proof of (a->(((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x02:((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))) (x020:((Xr Xx0) Xy0)) (x0200:((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))))=> (((fun (P:Type) (x1:((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0)))) P) x1) x02)) ((Xq Xx00) Xy0)) (fun (x1:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (x2:(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy00) Xy0))))=> ((x1 x020) x0200)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))))))
% Found x100:=(x10 x030):((Xq Xx00) Xy00)
% Found (x10 x030) as proof of ((Xq Xx00) Xy00)
% Found ((x1 Xy00) x030) as proof of ((Xq Xx00) Xy00)
% Found (fun (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)) as proof of ((Xq Xx00) Xy00)
% Found (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00))
% Found (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00)))
% Found (and_rect10 (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found ((and_rect1 ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (fun (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of ((Xq Xx00) Xy00)
% Found (fun (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (((Xr Xx0) Xy00)->((Xq Xx00) Xy00))
% Found (fun (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x1 Xy00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found x0400:=(x040 x020):((x Xx0) Xz0)
% Found (x040 x020) as proof of ((x Xx0) Xz0)
% Found ((x04 Xy00) x020) as proof of ((x Xx0) Xz0)
% Found (fun (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)) as proof of ((x Xx0) Xz0)
% Found (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->((x Xx0) Xz0))
% Found (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->((x Xx0) Xz0)))
% Found (and_rect10 (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020))) as proof of ((x Xx0) Xz0)
% Found ((and_rect1 ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020))) as proof of ((x Xx0) Xz0)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020))) as proof of ((x Xx0) Xz0)
% Found (fun (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)))) as proof of ((x Xx0) Xz0)
% Found (fun (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)))) as proof of (((Xr Xx0) Xy00)->((x Xx0) Xz0))
% Found (fun (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx0) Xz0)))
% Found (fun (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))) (Xy00:a) (x020:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0)))) P) x1) x02)) ((x Xx0) Xz0)) (fun (x03:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (x04:(forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))=> ((x04 Xy00) x020)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((x Xx0) Xz0))))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x1:((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xy00) Xy0))=> x1) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x2:((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xz0))=> x2) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x3:((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xz0))=> x3) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x2:((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xy00) Xy0))=> x2) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x1000:=(x100 x020):((Xq Xx00) Xy00)
% Found (x100 x020) as proof of ((Xq Xx00) Xy00)
% Found ((x10 Xy00) x020) as proof of ((Xq Xx00) Xy00)
% Found (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020) as proof of ((Xq Xx00) Xy00)
% Found (fun (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)) as proof of ((Xq Xx00) Xy00)
% Found (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000))))->((Xq Xx00) Xy00))
% Found (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000))))->((Xq Xx00) Xy00)))
% Found (and_rect10 (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020))) as proof of ((Xq Xx00) Xy00)
% Found ((and_rect1 ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020))) as proof of ((Xq Xx00) Xy00)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020))) as proof of ((Xq Xx00) Xy00)
% Found (fun (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of ((Xq Xx00) Xy00)
% Found (fun (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))
% Found (fun (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00)))
% Found (fun (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))))
% Found (fun (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0)))))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0)))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xy0) Xy00))))) P) x1) x02)) ((Xq Xx00) Xy00)) (fun (x1:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xx00) Xy000))))) (x2:(forall (Xy000:a), (((Xr Xx0) Xy000)->(((and (forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xq Xx000) Xy0000)) ((Xq Xy0000) Xz00))->((Xq Xx000) Xz00)))) (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xq Xx000) Xy0000))))->((Xq Xy0) Xy000)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x1 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000))))->((Xq Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))) (forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))->((Xq Xx00) Xy0)))))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x2:((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xz0))=> x2) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((Xq Xx0) Xy00)) (x2:((Xq Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x1:((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xy00) Xy0))=> x1) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((Xq Xx00) Xy0)) (x2:((Xq Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x2:((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xy00) Xy0))=> x2) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((Xq Xx00) Xy0)) (x3:((Xq Xy00) Xy0))=> x2))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x3:((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xz0))=> x3) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((Xq Xx0) Xy00)) (x3:((Xq Xx0) Xz0))=> x3))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x200:=(x20 x030):((Xq Xx0) Xz0)
% Found (x20 x030) as proof of ((Xq Xx0) Xz0)
% Found ((x2 Xy00) x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0))
% Found (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))
% Found (fun (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x200:=(x20 x030):((Xq Xx0) Xz0)
% Found (x20 x030) as proof of ((Xq Xx0) Xz0)
% Found ((x2 Xy00) x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0))
% Found (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))
% Found (fun (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))=> ((x2 Xy00) x030)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))))
% Found x04000:=(x0400 x020):((x Xx00) Xz0)
% Found (x0400 x020) as proof of ((x Xx00) Xz0)
% Found ((x040 Xy00) x020) as proof of ((x Xx00) Xz0)
% Found (((x04 Xx00) Xy00) x020) as proof of ((x Xx00) Xz0)
% Found (fun (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)) as proof of ((x Xx00) Xz0)
% Found (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0)))->((x Xx00) Xz0))
% Found (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0)))->((x Xx00) Xz0)))
% Found (and_rect10 (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020))) as proof of ((x Xx00) Xz0)
% Found ((and_rect1 ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020))) as proof of ((x Xx00) Xz0)
% Found (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020))) as proof of ((x Xx00) Xz0)
% Found (fun (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of ((x Xx00) Xz0)
% Found (fun (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of (((Xr Xx00) Xy00)->((x Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((x Xx00) Xz0)))
% Found (fun (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx00) Xz0)))
% Found (fun (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx00) Xz0)))) P) x1) x02)) ((x Xx00) Xz0)) (fun (x03:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xy0)))) (x04:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((x Xx000) Xz0))))=> (((x04 Xx00) Xy00) x020)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xx0) Xz0))))->(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((x Xx0) Xz0))))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x20:=(x2 x200):((Xq Xx00) Xy0)
% Found (x2 x200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))))
% Found x20:=(x2 x200):((Xq Xx00) Xy0)
% Found (x2 x200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0)))))
% Found x30:=(x3 x200):((Xq Xx0) Xz0)
% Found (x3 x200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x200:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1)))->((Xq Xx0) Xz0)))))
% Found x30:=(x3 x200):((Xq Xx0) Xz0)
% Found (x3 x200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found x10:=(x1 x20):((Xq Xx00) Xy0)
% Found (x1 x20) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))))
% Found x21:=(x2 x20):((Xq Xx0) Xz0)
% Found (x2 x20) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found x30:=(x3 x200):((Xq Xx0) Xz0)
% Found (x3 x200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found x30:=(x3 x030):((Xq Xx00) Xy0)
% Found (x3 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x40:=(x4 x030):((Xq Xx0) Xz0)
% Found (x4 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x20:=(x2 x200):((Xq Xx00) Xy0)
% Found (x2 x200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x40:=(x4 x030):((Xq Xx0) Xz0)
% Found (x4 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x30:=(x3 x030):((Xq Xx00) Xy0)
% Found (x3 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x4:((Xq Xx0) Xz0)
% Found (fun (x4:((Xq Xx0) Xz0))=> x4) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xz0)->((Xq Xx0) Xz0))
% Found (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4) as proof of (((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of ((Xq Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xq Xx0) Xy00)->(((Xq Xx0) Xz0)->P)))=> (((((and_rect ((Xq Xx0) Xy00)) ((Xq Xx0) Xz0)) P) x3) x04)) ((Xq Xx0) Xz0)) (fun (x3:((Xq Xx0) Xy00)) (x4:((Xq Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xq Xx0) Xy0)) ((Xq Xx0) Xz0))->((Xq Xx0) Xz0))))
% Found x3:((Xq Xx00) Xy0)
% Found (fun (x4:((Xq Xy00) Xy0))=> x3) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xy00) Xy0)->((Xq Xx00) Xy0))
% Found (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3) as proof of (((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of ((Xq Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xq Xx00) Xy0)->(((Xq Xy00) Xy0)->P)))=> (((((and_rect ((Xq Xx00) Xy0)) ((Xq Xy00) Xy0)) P) x3) x04)) ((Xq Xx00) Xy0)) (fun (x3:((Xq Xx00) Xy0)) (x4:((Xq Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xq Xx0) Xy0)) ((Xq Xy00) Xy0))->((Xq Xx0) Xy0))))
% Found x03000:=(x0300 x020):((x Xx0) Xy00)
% Found (x0300 x020) as proof of ((x Xx0) Xy00)
% Found ((x030 Xx00) x020) as proof of ((x Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020) as proof of ((x Xx0) Xy00)
% Found (fun (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)) as proof of ((x Xx0) Xy00)
% Found (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000)))->((x Xx0) Xy00))
% Found (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000)))->((x Xx0) Xy00)))
% Found (and_rect10 (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020))) as proof of ((x Xx0) Xy00)
% Found ((and_rect1 ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020))) as proof of ((x Xx0) Xy00)
% Found (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020))) as proof of ((x Xx0) Xy00)
% Found (fun (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of ((x Xx0) Xy00)
% Found (fun (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of (((Xr Xx00) Xy00)->((x Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((x Xx0) Xy0)))
% Found (fun (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx0) Xy0)))
% Found (fun (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x020:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xy0) Xy00)))) P) x1) x02)) ((x Xx0) Xy00)) (fun (x03:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xx0) Xy000)))) (x04:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((x Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x03 Xx000) Xy00)) Xx00) x020)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((x Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((x Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((x Xx0) Xy0))))))
% Found x30:=(x3 x030):((Xq Xx00) Xy0)
% Found (x3 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x40:=(x4 x030):((Xq Xx0) Xz0)
% Found (x4 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x21:=(x2 x20):((Xq Xx0) Xz0)
% Found (x2 x20) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x2 x20)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found x10:=(x1 x20):((Xq Xx00) Xy0)
% Found (x1 x20) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x1 x20)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))))
% Found x30:=(x3 x030):((Xq Xx00) Xy0)
% Found (x3 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x30:=(x3 x200):((Xq Xx0) Xz0)
% Found (x3 x200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found x20:=(x2 x200):((Xq Xx00) Xy0)
% Found (x2 x200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))))
% Found x40:=(x4 x030):((Xq Xx0) Xz0)
% Found (x4 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x2000:=(x200 x020):((Xq Xx0) Xz0)
% Found (x200 x020) as proof of ((Xq Xx0) Xz0)
% Found ((x20 Xy00) x020) as proof of ((Xq Xx0) Xz0)
% Found (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->((Xq Xx0) Xz0))
% Found (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->((Xq Xx0) Xz0)))
% Found (and_rect10 (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect1 ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))
% Found (fun (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))
% Found (fun (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0))))
% Found (fun (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))))
% Found (fun (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0))))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0))))))
% Found (fun (Xx1:a) (Xy0:a) (Xz0:a) (x02:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))) (Xy00:a) (x020:((Xr Xx0) Xy00)) (x0200:((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))))=> (((fun (P:Type) (x1:((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0))))) P) x1) x02)) ((Xq Xx0) Xz0)) (fun (x1:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (x2:(forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))=> (((fun (Xy000:a) (x0201:((Xr Xx0) Xy000))=> (((x2 Xy000) x0201) x0200)) Xy00) x020)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->(((and (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))->((Xq Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->(((and (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))->((Xq Xx0) Xz0)))))))
% Found x2000:=(x200 x030):((Xq Xx00) Xz0)
% Found (x200 x030) as proof of ((Xq Xx00) Xz0)
% Found ((x20 Xy00) x030) as proof of ((Xq Xx00) Xz0)
% Found (((x2 Xx00) Xy00) x030) as proof of ((Xq Xx00) Xz0)
% Found (fun (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)) as proof of ((Xq Xx00) Xz0)
% Found (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0)))->((Xq Xx00) Xz0))
% Found (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0)))->((Xq Xx00) Xz0)))
% Found (and_rect10 (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030))) as proof of ((Xq Xx00) Xz0)
% Found ((and_rect1 ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030))) as proof of ((Xq Xx00) Xz0)
% Found (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030))) as proof of ((Xq Xx00) Xz0)
% Found (fun (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of ((Xq Xx00) Xz0)
% Found (fun (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))
% Found (fun (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))))
% Found x2000:=(x200 x030):((Xq Xx00) Xz0)
% Found (x200 x030) as proof of ((Xq Xx00) Xz0)
% Found ((x20 Xy00) x030) as proof of ((Xq Xx00) Xz0)
% Found (((x2 Xx00) Xy00) x030) as proof of ((Xq Xx00) Xz0)
% Found (fun (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)) as proof of ((Xq Xx00) Xz0)
% Found (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0)))->((Xq Xx00) Xz0))
% Found (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0)))->((Xq Xx00) Xz0)))
% Found (and_rect10 (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030))) as proof of ((Xq Xx00) Xz0)
% Found ((and_rect1 ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030))) as proof of ((Xq Xx00) Xz0)
% Found (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030))) as proof of ((Xq Xx00) Xz0)
% Found (fun (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of ((Xq Xx00) Xz0)
% Found (fun (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))
% Found (fun (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xz0)))) P) x1) x03)) ((Xq Xx00) Xz0)) (fun (x1:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy0)))) (x2:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xz0))))=> (((x2 Xx00) Xy00) x030)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx0) Xz0))))->(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))))
% Found x30:=(x3 x030):((Xq Xx00) Xy0)
% Found (x3 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x30:=(x3 x200):((Xq Xx0) Xz0)
% Found (x3 x200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))))
% Found x20:=(x2 x200):((Xq Xx00) Xy0)
% Found (x2 x200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0)))))
% Found x40:=(x4 x030):((Xq Xx0) Xz0)
% Found (x4 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x40:=(x4 x030):((Xq Xx0) Xz0)
% Found (x4 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x30:=(x3 x030):((Xq Xx00) Xy0)
% Found (x3 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x20:=(x2 Xx0):(forall (Xy:a), (((Xr Xx0) Xy)->((Xq Xx0) Xy)))
% Found (x2 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))
% Found (x2 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x03)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x03:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x03)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x03)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x03)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x03)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x03)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x03)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x03:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x03)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x03:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x03)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x03)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x03)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x03)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x2:((Xr Xx0) Xz0)
% Found (fun (x2:((Xr Xx0) Xz0))=> x2) as proof of ((Xr Xx0) Xz0)
% Found (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x1:((Xr Xx00) Xy0)
% Found (fun (x2:((Xr Xy00) Xy0))=> x1) as proof of ((Xr Xx00) Xy0)
% Found (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x2:((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xy00) Xy0))=> x2) as proof of ((Xr Xx00) Xy0)
% Found (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x3:((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xz0))=> x3) as proof of ((Xr Xx0) Xz0)
% Found (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x02:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x02 as proof of ((Xr Xy00) Xy0)
% Found (x200 x02) as proof of ((Xq Xy00) Xy0)
% Found ((x20 Xy0) x02) as proof of ((Xq Xy00) Xy0)
% Found (((x2 Xy00) Xy0) x02) as proof of ((Xq Xy00) Xy0)
% Found (((x2 Xy00) Xy0) x02) as proof of ((Xq Xy00) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x03 as proof of ((Xr Xy00) Xy0)
% Found (x2000 x03) as proof of ((Xq Xy00) Xy0)
% Found ((x200 Xy0) x03) as proof of ((Xq Xy00) Xy0)
% Found (((x20 Xy00) Xy0) x03) as proof of ((Xq Xy00) Xy0)
% Found (((x20 Xy00) Xy0) x03) as proof of ((Xq Xy00) Xy0)
% Found x02:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x02 as proof of ((Xr Xx0) Xy00)
% Found (x200 x02) as proof of ((Xq Xx0) Xy00)
% Found ((x20 Xy00) x02) as proof of ((Xq Xx0) Xy00)
% Found (((x2 Xx0) Xy00) x02) as proof of ((Xq Xx0) Xy00)
% Found (((x2 Xx0) Xy00) x02) as proof of ((Xq Xx0) Xy00)
% Found x02:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xx0:a
% Found x02 as proof of ((Xr Xy1) Xy0)
% Found (x200 x02) as proof of ((Xq Xy1) Xy0)
% Found ((x20 Xy0) x02) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x02) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x02) as proof of ((Xq Xy1) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy00)
% Found (x2000 x03) as proof of ((Xq Xx0) Xy00)
% Found ((x200 Xy00) x03) as proof of ((Xq Xx0) Xy00)
% Found (((x20 Xx0) Xy00) x03) as proof of ((Xq Xx0) Xy00)
% Found (((x20 Xx0) Xy00) x03) as proof of ((Xq Xx0) Xy00)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xx0:a
% Found x03 as proof of ((Xr Xy1) Xy0)
% Found (x20000 x03) as proof of ((Xq Xy1) Xy0)
% Found ((x2000 Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x200 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x200 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found x02:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xy0:a
% Found x02 as proof of ((Xr Xx0) Xy1)
% Found (x200 x02) as proof of ((Xq Xx0) Xy1)
% Found ((x20 Xy1) x02) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x02) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x02) as proof of ((Xq Xx0) Xy1)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xx0:a
% Found x03 as proof of ((Xr Xy1) Xy0)
% Found (x200 x03) as proof of ((Xq Xy1) Xy0)
% Found ((x20 Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy1)
% Found (x20000 x03) as proof of ((Xq Xx0) Xy1)
% Found ((x2000 Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x200 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x200 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy1)
% Found (x200 x03) as proof of ((Xq Xx0) Xy1)
% Found ((x20 Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found x210:=(x21 x20):((Xq Xx0) Xz0)
% Found (x21 x20) as proof of ((Xq Xx0) Xz0)
% Found ((x2 x100) x20) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0))
% Found (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))
% Found (fun (x03:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x03)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))))
% Found x300:=(x30 x030):((Xq Xx00) Xy00)
% Found (x30 x030) as proof of ((Xq Xx00) Xy00)
% Found ((x3 Xy00) x030) as proof of ((Xq Xx00) Xy00)
% Found (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)) as proof of ((Xq Xx00) Xy00)
% Found (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00))
% Found (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00)))
% Found (and_rect20 (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found ((and_rect2 ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (fun (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of ((Xq Xx00) Xy00)
% Found (fun (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (((Xr Xx0) Xy00)->((Xq Xx00) Xy00))
% Found (fun (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found x101:=(x10 x20):((Xq Xx00) Xy0)
% Found (x10 x20) as proof of ((Xq Xx00) Xy0)
% Found ((x1 x100) x20) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0))
% Found (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (x03:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x03)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy0)))) ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))))))
% Found x210:=(x21 x20):((Xq Xx0) Xz0)
% Found (x21 x20) as proof of ((Xq Xx0) Xz0)
% Found ((x2 x100) x20) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0))
% Found (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))
% Found (fun (x04:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))) (x20:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000))))=> (((fun (P:Type) (x1:(((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx00) Xz00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))))
% Found x101:=(x10 x20):((Xq Xx00) Xy0)
% Found (x10 x20) as proof of ((Xq Xx00) Xy0)
% Found ((x1 x100) x20) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0))
% Found (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (x04:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xq Xx000) Xy00)) ((Xq Xy00) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xq Xx000) Xy000)) ((Xq Xy000) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy0)))) ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xq Xx00) Xy000)) ((Xq Xy000) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xq Xx00) Xy00)) ((Xq Xy00) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xy0))))))
% Found x210:=(x21 x20):((Xq Xx0) Xz0)
% Found (x21 x20) as proof of ((Xq Xx0) Xz0)
% Found ((x2 x100) x20) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0))
% Found (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)) as proof of (((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x20:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x100:(forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (x20:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))
% Found (fun (x04:((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (x20:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (x20:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))->((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (x20:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xz0:a), (((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))->((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (x20:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy0)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))->((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))) (x100:(forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))) (x20:(forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx10:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx10) Xz0)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))->(((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) ((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0)))) P) x1) x04)) ((Xq Xx0) Xz0)) (fun (x1:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xy00)))) (x2:((forall (Xx10:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx10) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx10) Xz00)))->((forall (Xx10:a) (Xy1:a), (((Xr Xx10) Xy1)->((Xq Xx10) Xy1)))->((Xq Xx0) Xz0))))=> ((x2 x100) x20)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx1:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx1) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx1) Xz0)))->((forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1)))->((Xq Xx0) Xy0)))) ((forall (Xx1:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx1) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx1) Xz00)))->((forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1)))->((Xq Xx0) Xz0))))->((forall (Xx1:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx1) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx1) Xz00)))->((forall (Xx1:a) (Xy1:a), (((Xr Xx1) Xy1)->((Xq Xx1) Xy1)))->((Xq Xx0) Xz0))))))
% Found x101:=(x10 x20):((Xq Xx00) Xy0)
% Found (x10 x20) as proof of ((Xq Xx00) Xy0)
% Found ((x1 x100) x20) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of (((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0))
% Found (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)) as proof of (((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x20:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x100:(forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))
% Found (fun (x04:((and ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (((and ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (a->(((and ((forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))->((forall (Xx000:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx000) Xz0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))) (x100:(forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))) (x20:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x1:(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))->(((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) ((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) P) x1) x04)) ((Xq Xx00) Xy0)) (fun (x1:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))) (x2:((forall (Xx000:a) (Xy1:a) (Xz00:a), (((and ((Xq Xx000) Xy1)) ((Xq Xy1) Xz00))->((Xq Xx000) Xz00)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))))=> ((x1 x100) x20)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx00) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0)))) ((forall (Xx00:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx00) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xy00) Xy0))))->((forall (Xx00:a) (Xy1:a) (Xz0:a), (((and ((Xq Xx00) Xy1)) ((Xq Xy1) Xz0))->((Xq Xx00) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))))))
% Found x300:=(x30 x200):((Xq Xx0) Xz0)
% Found (x30 x200) as proof of ((Xq Xx0) Xz0)
% Found ((x3 x030) x200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0))
% Found (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)))) as proof of ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)))) as proof of (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)))) as proof of (((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0)))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0)))) P) x2) x03)) ((Xq Xx0) Xz0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))=> ((x3 x030) x200)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx00) Xy00)))->((Xq Xx0) Xz0))))))
% Found x201:=(x20 x200):((Xq Xx00) Xy0)
% Found (x20 x200) as proof of ((Xq Xx00) Xy0)
% Found ((x2 x030) x200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0))
% Found (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)))) as proof of (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)))) as proof of (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))) (x030:((Xr Xx0) Xy0)) (x200:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00))))=> (((fun (P:Type) (x2:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0)))) P) x2) x03)) ((Xq Xx00) Xy0)) (fun (x2:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (x3:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xy00) Xy0))))=> ((x2 x030) x200)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xq Xx000) Xy000)))->((Xq Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx00) Xy000)))->((Xq Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xq Xx000) Xy00)))->((Xq Xx00) Xy0))))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x1000:=(x100 x030):((Xq Xx0) Xy00)
% Found (x100 x030) as proof of ((Xq Xx0) Xy00)
% Found ((x10 Xx00) x030) as proof of ((Xq Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030) as proof of ((Xq Xx0) Xy00)
% Found (fun (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)) as proof of ((Xq Xx0) Xy00)
% Found (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx0) Xy00))
% Found (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx0) Xy00)))
% Found (and_rect10 (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030))) as proof of ((Xq Xx0) Xy00)
% Found ((and_rect1 ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030))) as proof of ((Xq Xx0) Xy00)
% Found (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030))) as proof of ((Xq Xx0) Xy00)
% Found (fun (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of ((Xq Xx0) Xy00)
% Found (fun (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (((Xr Xx00) Xy00)->((Xq Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0)))
% Found (fun (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0))))))
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xx0:a
% Found x03 as proof of ((Xr Xy1) Xy0)
% Found (x200 x03) as proof of ((Xq Xy1) Xy0)
% Found ((x20 Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy1)
% Found (x200 x03) as proof of ((Xq Xx0) Xy1)
% Found ((x20 Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))
% Found (fun (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3) as proof of ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))
% Found (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3) as proof of (((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz)))
% Found (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3) as proof of (((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->(((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))))
% Found (and_rect20 (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3)) as proof of ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))
% Found ((and_rect2 ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3)) as proof of ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))
% Found (((fun (P:Type) (x3:(((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->(((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->P)))=> (((((and_rect ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))) P) x3) x03)) ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3)) as proof of ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))
% Found (fun (x03:((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))))=> (((fun (P:Type) (x3:(((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->(((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->P)))=> (((((and_rect ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))) P) x3) x03)) ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3))) as proof of ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))
% Found (fun (Xz0:a) (x03:((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))))=> (((fun (P:Type) (x3:(((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->(((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->P)))=> (((((and_rect ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))) P) x3) x03)) ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3))) as proof of (((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))->((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))))=> (((fun (P:Type) (x3:(((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->(((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->P)))=> (((((and_rect ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))) P) x3) x03)) ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3))) as proof of (a->(((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))->((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x03:((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))))=> (((fun (P:Type) (x3:(((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->(((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->P)))=> (((((and_rect ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))) P) x3) x03)) ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))->((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x03:((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))))=> (((fun (P:Type) (x3:(((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))->(((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))->P)))=> (((((and_rect ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz))) P) x3) x03)) ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (fun (x3:((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) (x4:((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz))) ((and ((Xq Xy00) Xy0)) ((Xq Xy0) Xz)))->((and ((Xq Xx0) Xy0)) ((Xq Xy0) Xz)))))
% Found x03:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x03 as proof of ((Xr Xx0) Xy0)
% Found (x200 x03) as proof of ((Xq Xx0) Xy0)
% Found ((x20 Xy0) x03) as proof of ((Xq Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x03) as proof of ((Xq Xx0) Xy0)
% Found (((x2 Xx0) Xy0) x03) as proof of ((Xq Xx0) Xy0)
% Found x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))
% Found (fun (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4) as proof of ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))
% Found (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))
% Found (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4) as proof of (((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))->(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))
% Found (and_rect20 (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4)) as proof of ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))
% Found ((and_rect2 ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4)) as proof of ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))
% Found (((fun (P:Type) (x3:(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))->(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) P) x3) x03)) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4)) as proof of ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))
% Found (fun (x03:((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))=> (((fun (P:Type) (x3:(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))->(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) P) x3) x03)) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4))) as proof of ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))
% Found (fun (Xz0:a) (x03:((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))=> (((fun (P:Type) (x3:(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))->(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) P) x3) x03)) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4))) as proof of (((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))->((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))=> (((fun (P:Type) (x3:(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))->(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) P) x3) x03)) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4))) as proof of (forall (Xz0:a), (((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))->((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x03:((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))=> (((fun (P:Type) (x3:(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))->(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) P) x3) x03)) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))->((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x03:((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))))=> (((fun (P:Type) (x3:(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))->(((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) P) x3) x03)) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0))) (fun (x3:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) (x4:((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))=> x4))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xy00))) ((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))->((and ((Xq Xx) Xy0)) ((Xq Xy0) Xz0)))))
% Found x03:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x03 as proof of ((Xr Xy0) Xy00)
% Found (x200 x03) as proof of ((Xq Xy0) Xy00)
% Found ((x20 Xy00) x03) as proof of ((Xq Xy0) Xy00)
% Found (((x2 Xy0) Xy00) x03) as proof of ((Xq Xy0) Xy00)
% Found (((x2 Xy0) Xy00) x03) as proof of ((Xq Xy0) Xy00)
% Found x300:=(x30 x030):((Xq Xx00) Xy00)
% Found (x30 x030) as proof of ((Xq Xx00) Xy00)
% Found ((x3 Xy00) x030) as proof of ((Xq Xx00) Xy00)
% Found (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)) as proof of ((Xq Xx00) Xy00)
% Found (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00))
% Found (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx00) Xy00)))
% Found (and_rect20 (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found ((and_rect2 ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030))) as proof of ((Xq Xx00) Xy00)
% Found (fun (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of ((Xq Xx00) Xy00)
% Found (fun (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (((Xr Xx0) Xy00)->((Xq Xx00) Xy00))
% Found (fun (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xy00:a) (x030:((Xr Xx0) Xy00))=> (((fun (P:Type) (x3:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))) P) x3) x03)) ((Xq Xx00) Xy00)) (fun (x3:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xx00) Xy000)))) (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xq Xy0) Xy000))))=> ((x3 Xy00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))))
% Found x1000:=(x100 x030):((Xq Xx0) Xy00)
% Found (x100 x030) as proof of ((Xq Xx0) Xy00)
% Found ((x10 Xx00) x030) as proof of ((Xq Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030) as proof of ((Xq Xx0) Xy00)
% Found (fun (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)) as proof of ((Xq Xx0) Xy00)
% Found (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx0) Xy00))
% Found (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000)))->((Xq Xx0) Xy00)))
% Found (and_rect10 (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030))) as proof of ((Xq Xx0) Xy00)
% Found ((and_rect1 ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030))) as proof of ((Xq Xx0) Xy00)
% Found (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030))) as proof of ((Xq Xx0) Xy00)
% Found (fun (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of ((Xq Xx0) Xy00)
% Found (fun (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (((Xr Xx00) Xy00)->((Xq Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0)))
% Found (fun (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0)))
% Found (fun (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x03:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x030:((Xr Xx00) Xy00))=> (((fun (P:Type) (x1:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xy0) Xy00)))) P) x1) x03)) ((Xq Xx0) Xy00)) (fun (x1:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xx0) Xy000)))) (x2:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xq Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x1 Xx000) Xy00)) Xx00) x030)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xq Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xq Xx0) Xy0))))))
% Found x30:=(x3 x200):((Xq Xx0) Xz0)
% Found (x3 x200) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)) as proof of (((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))) (x200:(forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))->(((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0))) P) x2) x04)) ((Xq Xx0) Xz0)) (fun (x2:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy00))) (x3:((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))=> (x3 x200)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xz0)))))
% Found x20:=(x2 x200):((Xq Xx00) Xy0)
% Found (x2 x200) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)) as proof of (((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (a->(((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))) (x200:(forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1))))=> (((fun (P:Type) (x2:(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))->(((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) ((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0))) P) x2) x04)) ((Xq Xx00) Xy0)) (fun (x2:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xx00) Xy0))) (x3:((forall (Xx000:a) (Xy1:a), (((Xr Xx000) Xy1)->((Xq Xx000) Xy1)))->((Xq Xy00) Xy0)))=> (x2 x200)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0))) ((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xy00) Xy0)))->((forall (Xx00:a) (Xy1:a), (((Xr Xx00) Xy1)->((Xq Xx00) Xy1)))->((Xq Xx0) Xy0)))))
% Found x20:=(x2 Xx0):(forall (Xy:a), (((Xr Xx0) Xy)->((Xq Xx0) Xy)))
% Found (x2 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))
% Found (x2 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))
% Found x30:=(x3 x030):((Xq Xx00) Xy0)
% Found (x3 x030) as proof of ((Xq Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((Xq Xx00) Xy0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->((Xq Xx00) Xy0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found ((and_rect2 ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of ((Xq Xx00) Xy0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xq Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0))) P) x3) x03)) ((Xq Xx00) Xy0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (x4:(((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))=> (x3 x030)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xq Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xq Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xq Xx00) Xy0)))))
% Found x40:=(x4 x030):((Xq Xx0) Xz0)
% Found (x4 x030) as proof of ((Xq Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((Xq Xx0) Xz0)
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0))
% Found (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)) as proof of ((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->((Xq Xx0) Xz0)))
% Found (and_rect20 (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found ((and_rect2 ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of ((Xq Xx0) Xz0)
% Found (fun (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))
% Found (fun (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0))))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x03:((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))) (x030:((Xr Xx0) Xy0))=> (((fun (P:Type) (x3:((((Xr Xx0) Xy0)->((Xq Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xq Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0))) P) x3) x03)) ((Xq Xx0) Xz0)) (fun (x3:(((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (x4:(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))=> (x4 x030)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xq Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xq Xx0) Xz0)))))
% Found x20:=(x2 Xx0):(forall (Xy:a), (((Xr Xx0) Xy)->((Xq Xx0) Xy)))
% Found (x2 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))
% Found (x2 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xq Xy0) Xy00)))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x2:((Xr Xx0) Xz0)
% Found (fun (x2:((Xr Xx0) Xz0))=> x2) as proof of ((Xr Xx0) Xz0)
% Found (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x1:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x1) x04)) ((Xr Xx0) Xz0)) (fun (x1:((Xr Xx0) Xy00)) (x2:((Xr Xx0) Xz0))=> x2))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x1:((Xr Xx00) Xy0)
% Found (fun (x2:((Xr Xy00) Xy0))=> x1) as proof of ((Xr Xx00) Xy0)
% Found (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x1:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x1) x04)) ((Xr Xx00) Xy0)) (fun (x1:((Xr Xx00) Xy0)) (x2:((Xr Xy00) Xy0))=> x1))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x4:((Xr Xx0) Xz0)
% Found (fun (x4:((Xr Xx0) Xz0))=> x4) as proof of ((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x3:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x3) x04)) ((Xr Xx0) Xz0)) (fun (x3:((Xr Xx0) Xy00)) (x4:((Xr Xx0) Xz0))=> x4))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x3:((Xr Xx00) Xy0)
% Found (fun (x4:((Xr Xy00) Xy0))=> x3) as proof of ((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x3:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x3) x04)) ((Xr Xx00) Xy0)) (fun (x3:((Xr Xx00) Xy0)) (x4:((Xr Xy00) Xy0))=> x3))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x2:((Xr Xx00) Xy0)
% Found (fun (x3:((Xr Xy00) Xy0))=> x2) as proof of ((Xr Xx00) Xy0)
% Found (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x2:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x2) x04)) ((Xr Xx00) Xy0)) (fun (x2:((Xr Xx00) Xy0)) (x3:((Xr Xy00) Xy0))=> x2))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x3:((Xr Xx0) Xz0)
% Found (fun (x3:((Xr Xx0) Xz0))=> x3) as proof of ((Xr Xx0) Xz0)
% Found (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx1:a) (Xy00:a) (Xz0:a) (x04:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x2:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x2) x04)) ((Xr Xx0) Xz0)) (fun (x2:((Xr Xx0) Xy00)) (x3:((Xr Xx0) Xz0))=> x3))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xx0:a
% Found x03 as proof of ((Xr Xy1) Xy0)
% Found (x200 x03) as proof of ((Xq Xy1) Xy0)
% Found ((x20 Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy1)
% Found (x200 x03) as proof of ((Xq Xx0) Xy1)
% Found ((x20 Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x03 as proof of ((Xr Xy00) Xy0)
% Found (x2000 x03) as proof of ((Xq Xy00) Xy0)
% Found ((x200 Xy0) x03) as proof of ((Xq Xy00) Xy0)
% Found (((x20 Xy00) Xy0) x03) as proof of ((Xq Xy00) Xy0)
% Found (((x20 Xy00) Xy0) x03) as proof of ((Xq Xy00) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xx0:a
% Found x03 as proof of ((Xr Xy1) Xy0)
% Found (x20000 x03) as proof of ((Xq Xy1) Xy0)
% Found ((x2000 Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x200 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x200 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy1)
% Found (x20000 x03) as proof of ((Xq Xx0) Xy1)
% Found ((x2000 Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x200 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x200 Xx0) Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy00)
% Found (x2000 x03) as proof of ((Xq Xx0) Xy00)
% Found ((x200 Xy00) x03) as proof of ((Xq Xx0) Xy00)
% Found (((x20 Xx0) Xy00) x03) as proof of ((Xq Xx0) Xy00)
% Found (((x20 Xx0) Xy00) x03) as proof of ((Xq Xx0) Xy00)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xx0:a
% Found x03 as proof of ((Xr Xy1) Xy0)
% Found (x200 x03) as proof of ((Xq Xy1) Xy0)
% Found ((x20 Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found (((x2 Xy1) Xy0) x03) as proof of ((Xq Xy1) Xy0)
% Found x03:((Xr Xx0) Xy0)
% Instantiate: Xy1:=Xy0:a
% Found x03 as proof of ((Xr Xx0) Xy1)
% Found (x200 x03) as proof of ((Xq Xx0) Xy1)
% Found ((x20 Xy1) x03) as proof of ((Xq Xx0) Xy1)
% Found (((x2 Xx0) Xy1) x03) as proo
% EOF
%------------------------------------------------------------------------------