TSTP Solution File: SEV099^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV099^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n094.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 13:33:44 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV099^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n094.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:03:46 CDT 2014
% % CPUTime : 300.03
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1dbc3b0>, <kernel.Type object at 0x1e38518>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))) (Xs:a) (Xt:a), (((and (((Xr Xs) Xt)->False)) (forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt))))->((ex a) (fun (Xz:a)=> ((and ((Xr Xs) Xz)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp Xz) Xt)))))))) of role conjecture named cTC_INTERP_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))) (Xs:a) (Xt:a), (((and (((Xr Xs) Xt)->False)) (forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt))))->((ex a) (fun (Xz:a)=> ((and ((Xr Xs) Xz)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp Xz) Xt)))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))) (Xs:a) (Xt:a), (((and (((Xr Xs) Xt)->False)) (forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt))))->((ex a) (fun (Xz:a)=> ((and ((Xr Xs) Xz)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp Xz) Xt))))))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))) (Xs:a) (Xt:a), (((and (((Xr Xs) Xt)->False)) (forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt))))->((ex a) (fun (Xz:a)=> ((and ((Xr Xs) Xz)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp Xz) Xt))))))))
% Found x1:(forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt)))
% Instantiate: x2:=Xs:a
% Found x1 as proof of (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x2) Xt)))
% Found x2:(forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt)))
% Instantiate: x0:=Xs:a
% Found x2 as proof of (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x0) Xt)))
% Found x1:(forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt)))
% Instantiate: x2:=Xs:a
% Found x1 as proof of (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x2) Xt)))
% Found x2:(forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt)))
% Instantiate: x0:=Xs:a
% Found x2 as proof of (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x0) Xt)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x2:=Xy:a
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) x2)
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))
% Found (x10 ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))))) as proof of ((ex a) (fun (Xz:a)=> ((and ((Xr Xs) Xz)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp Xz) Xt))))))
% Found ((x1 (fun (x4:a) (x30:a)=> ((ex a) (fun (Xz:a)=> ((and ((Xr x4) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp0 Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 Xz) x30)))))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))))) as proof of ((ex a) (fun (Xz:a)=> ((and ((Xr Xs) Xz)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp Xz) Xt))))))
% Found ((x1 (fun (x4:a) (x30:a)=> ((ex a) (fun (Xz:a)=> ((and ((Xr x4) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp0 Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 Xz) x30)))))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx) Xz00))))->((Xp0 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))))) as proof of ((ex a) (fun (Xz:a)=> ((and ((Xr Xs) Xz)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp Xz) Xt))))))
% Found x2:((Xr Xx) Xy)
% Found (fun (x2:((Xr Xx) Xy))=> x2) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x2:((Xr Xx) Xy))=> x2) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x2:((Xr Xx) Xy))=> x2) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x2:((Xr Xx) Xy))=> x2) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xy:a
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) x0)
% Found x3:((Xr Xx) Xy)
% Instantiate: x2:=Xy:a
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) x2)
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xy:a
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) x0)
% Found x3:((Xr Xx) Xy)
% Instantiate: x2:=Xy:a
% Found x3 as proof of ((Xr Xx) x2)
% Found x1:(forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt)))
% Instantiate: x2:=Xs:a
% Found x1 as proof of (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x2) Xt)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xy:a
% Found x3 as proof of ((Xr Xx) x0)
% Found x3:((Xr Xx) Xy)
% Instantiate: x2:=Xy:a
% Found x3 as proof of ((Xr Xx) x2)
% Found x2:(forall (Xp:(a->(a->Prop))), (((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))))->((Xp Xs) Xt)))
% Instantiate: x0:=Xs:a
% Found x2 as proof of (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x0) Xt)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xy:a
% Found x3 as proof of ((Xr Xx) x0)
% Found x2:((Xr Xx) Xy)
% Instantiate: x3:=Xy:a
% Found x2 as proof of ((Xr Xx) x3)
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))
% Found (x10 ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of ((and ((Xr Xs) x2)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x2) Xt))))
% Found ((x1 (fun (x5:a) (x40:a)=> ((and ((Xr x5) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp0 Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) x40)))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of ((and ((Xr Xs) x2)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x2) Xt))))
% Found ((x1 (fun (x5:a) (x40:a)=> ((and ((Xr x5) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp0 Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) x40)))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of ((and ((Xr Xs) x2)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x2) Xt))))
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x2:((Xr Xx) Xy)
% Instantiate: x3:=Xy:a
% Found x2 as proof of ((Xr Xx) x3)
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of ((and ((Xr Xs) x0)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x0) Xt))))
% Found ((x2 (fun (x5:a) (x40:a)=> ((and ((Xr x5) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp0 Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) x40)))))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of ((and ((Xr Xs) x0)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x0) Xt))))
% Found ((x2 (fun (x5:a) (x40:a)=> ((and ((Xr x5) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp0 Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) x40)))))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of ((and ((Xr Xs) x0)) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0))))->((Xp x0) Xt))))
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x4:((Xr Xx) x2)
% Found (fun (x5:((Xr Xy) x2))=> x4) as proof of ((Xr Xx) x2)
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xy) x2)->((Xr Xx) x2))
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xx) x2)->(((Xr Xy) x2)->((Xr Xx) x2)))
% Found (and_rect10 (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found ((and_rect1 ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (fun (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of ((Xr Xx) x2)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found x4:((Xr Xx) x2)
% Found (fun (x5:((Xr Xy) x2))=> x4) as proof of ((Xr Xx) x2)
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xy) x2)->((Xr Xx) x2))
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xx) x2)->(((Xr Xy) x2)->((Xr Xx) x2)))
% Found (and_rect10 (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found ((and_rect1 ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (fun (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of ((Xr Xx) x2)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found x4:((Xr Xx) Xx)
% Found (fun (x5:((Xr Xy) Xy))=> x4) as proof of ((Xr Xx) Xx)
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xy) Xy)->((Xr Xx) Xx))
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xx) Xx)->(((Xr Xy) Xy)->((Xr Xx) Xx)))
% Found (and_rect10 (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found ((and_rect1 ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (fun (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of ((Xr Xx) Xx)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found x4:((Xr Xx) x0)
% Found (fun (x5:((Xr Xy) x0))=> x4) as proof of ((Xr Xx) x0)
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xy) x0)->((Xr Xx) x0))
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xx) x0)->(((Xr Xy) x0)->((Xr Xx) x0)))
% Found (and_rect10 (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found ((and_rect1 ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (fun (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of ((Xr Xx) x0)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found x4:((Xr Xx) x2)
% Found (fun (x5:((Xr Xy) x2))=> x4) as proof of ((Xr Xx) x2)
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xy) x2)->((Xr Xx) x2))
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xx) x2)->(((Xr Xy) x2)->((Xr Xx) x2)))
% Found (and_rect10 (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found ((and_rect1 ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (fun (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of ((Xr Xx) x2)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found x4:((Xr Xx) x0)
% Found (fun (x5:((Xr Xy) x0))=> x4) as proof of ((Xr Xx) x0)
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xy) x0)->((Xr Xx) x0))
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xx) x0)->(((Xr Xy) x0)->((Xr Xx) x0)))
% Found (and_rect10 (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found ((and_rect1 ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (fun (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of ((Xr Xx) x0)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found x4:((Xr Xx) Xx)
% Found (fun (x5:((Xr Xy) Xy))=> x4) as proof of ((Xr Xx) Xx)
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xy) Xy)->((Xr Xx) Xx))
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xx) Xx)->(((Xr Xy) Xy)->((Xr Xx) Xx)))
% Found (and_rect10 (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found ((and_rect1 ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (fun (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of ((Xr Xx) Xx)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found x4:((Xr Xx) x2)
% Found (fun (x5:((Xr Xy) x2))=> x4) as proof of ((Xr Xx) x2)
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xy) x2)->((Xr Xx) x2))
% Found (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4) as proof of (((Xr Xx) x2)->(((Xr Xy) x2)->((Xr Xx) x2)))
% Found (and_rect10 (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found ((and_rect1 ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4)) as proof of ((Xr Xx) x2)
% Found (fun (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of ((Xr Xx) x2)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x2)) ((Xr Xy) x2)))=> (((fun (P:Type) (x4:(((Xr Xx) x2)->(((Xr Xy) x2)->P)))=> (((((and_rect ((Xr Xx) x2)) ((Xr Xy) x2)) P) x4) x3)) ((Xr Xx) x2)) (fun (x4:((Xr Xx) x2)) (x5:((Xr Xy) x2))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))
% Found x4:((Xr Xx) Xx)
% Found (fun (x5:((Xr Xy) Xy))=> x4) as proof of ((Xr Xx) Xx)
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xy) Xy)->((Xr Xx) Xx))
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xx) Xx)->(((Xr Xy) Xy)->((Xr Xx) Xx)))
% Found (and_rect10 (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found ((and_rect1 ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (fun (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of ((Xr Xx) Xx)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found (x10 ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))))) as proof of ((Xr Xs) x2)
% Found ((x1 (fun (x5:a) (x40:a)=> ((Xr x5) x2))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))))) as proof of ((Xr Xs) x2)
% Found ((x1 (fun (x5:a) (x40:a)=> ((Xr x5) x2))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))))) as proof of ((Xr Xs) x2)
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x4:((Xr Xx) x0)
% Found (fun (x5:((Xr Xy) x0))=> x4) as proof of ((Xr Xx) x0)
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xy) x0)->((Xr Xx) x0))
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xx) x0)->(((Xr Xy) x0)->((Xr Xx) x0)))
% Found (and_rect10 (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found ((and_rect1 ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (fun (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of ((Xr Xx) x0)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2)))))
% Found (x10 ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))))) as proof of ((Xr Xs) x2)
% Found ((x1 (fun (x5:a) (x40:a)=> ((Xr x5) x2))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))))) as proof of ((Xr Xs) x2)
% Found ((x1 (fun (x5:a) (x40:a)=> ((Xr x5) x2))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x2)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x2)) ((Xr Xy) x2))->((Xr Xx) x2))))))) as proof of ((Xr Xs) x2)
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x4:((Xr Xx) x0)
% Found (fun (x5:((Xr Xy) x0))=> x4) as proof of ((Xr Xx) x0)
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xy) x0)->((Xr Xx) x0))
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xx) x0)->(((Xr Xy) x0)->((Xr Xx) x0)))
% Found (and_rect10 (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found ((and_rect1 ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (fun (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of ((Xr Xx) x0)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found x4:((Xr Xx) Xx)
% Found (fun (x5:((Xr Xy) Xy))=> x4) as proof of ((Xr Xx) Xx)
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xy) Xy)->((Xr Xx) Xx))
% Found (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4) as proof of (((Xr Xx) Xx)->(((Xr Xy) Xy)->((Xr Xx) Xx)))
% Found (and_rect10 (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found ((and_rect1 ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4)) as proof of ((Xr Xx) Xx)
% Found (fun (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of ((Xr Xx) Xx)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) Xx)) ((Xr Xy) Xy)))=> (((fun (P:Type) (x4:(((Xr Xx) Xx)->(((Xr Xy) Xy)->P)))=> (((((and_rect ((Xr Xx) Xx)) ((Xr Xy) Xy)) P) x4) x3)) ((Xr Xx) Xx)) (fun (x4:((Xr Xx) Xx)) (x5:((Xr Xy) Xy))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) Xx)) ((Xr Xy) Xy))->((Xr Xx) Xx))))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found ((x2 (fun (x5:a) (x40:a)=> ((Xr x5) x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found ((x2 (fun (x5:a) (x40:a)=> ((Xr x5) x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xy:a
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) x0)
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found ((x2 (fun (x5:a) (x40:a)=> ((Xr x5) x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found ((x2 (fun (x5:a) (x40:a)=> ((Xr x5) x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xy:a
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) x0)
% Found x3:((Xr Xx) Xy)
% Instantiate: x2:=Xx:a
% Found x3 as proof of ((Xr x2) Xy)
% Found (x400 x3) as proof of ((Xp0 x2) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 x2) Xy)
% Found (((x4 x2) Xy) x3) as proof of ((Xp0 x2) Xy)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)) as proof of ((Xp0 x2) Xy)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x2) Xy))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x2) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3))) as proof of ((Xp0 x2) Xy)
% Found ((and_rect1 ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3))) as proof of ((Xp0 x2) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3))) as proof of ((Xp0 x2) Xy)
% Found (fun (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)))) as proof of ((Xp0 x2) Xy)
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)))) as proof of (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x3 as proof of ((Xr x0) Xy)
% Found (x400 x3) as proof of ((Xp0 x0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 x0) Xy)
% Found (((x4 x0) Xy) x3) as proof of ((Xp0 x0) Xy)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((Xp0 x0) Xy)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x0) Xy))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x0) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp0 x0) Xy)
% Found ((and_rect1 ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp0 x0) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp0 x0) Xy)
% Found (fun (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of ((Xp0 x0) Xy)
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x2:=Xx:a
% Found x3 as proof of ((Xr x2) Xy)
% Found (x400 x3) as proof of ((Xp0 x2) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 x2) Xy)
% Found (((x4 x2) Xy) x3) as proof of ((Xp0 x2) Xy)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)) as proof of ((Xp0 x2) Xy)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x2) Xy))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x2) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3))) as proof of ((Xp0 x2) Xy)
% Found ((and_rect1 ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3))) as proof of ((Xp0 x2) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3))) as proof of ((Xp0 x2) Xy)
% Found (fun (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)))) as proof of ((Xp0 x2) Xy)
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)))) as proof of (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x2) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x2) Xy) x3)))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found ((x2 (fun (x5:a) (x40:a)=> ((Xr x5) x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found ((x2 (fun (x5:a) (x40:a)=> ((Xr x5) x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) x0)))) (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))))) as proof of ((Xr Xs) x0)
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x3 as proof of ((Xr x0) Xy)
% Found (x400 x3) as proof of ((Xp0 x0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 x0) Xy)
% Found (((x4 x0) Xy) x3) as proof of ((Xp0 x0) Xy)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((Xp0 x0) Xy)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x0) Xy))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x0) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp0 x0) Xy)
% Found ((and_rect1 ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp0 x0) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp0 x0) Xy)
% Found (fun (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of ((Xp0 x0) Xy)
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x0) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))
% Found x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))
% Found x7 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))
% Found x2:((Xr Xx) Xy)
% Instantiate: x3:=Xx:a
% Found x2 as proof of ((Xr x3) Xy)
% Found (x410 x2) as proof of ((Xp0 x3) Xy)
% Found ((x41 Xy) x2) as proof of ((Xp0 x3) Xy)
% Found (((x4 x3) Xy) x2) as proof of ((Xp0 x3) Xy)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)) as proof of ((Xp0 x3) Xy)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x3) Xy))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x3) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2))) as proof of ((Xp0 x3) Xy)
% Found ((and_rect1 ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2))) as proof of ((Xp0 x3) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x40)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2))) as proof of ((Xp0 x3) Xy)
% Found (fun (x40:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x40)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)))) as proof of ((Xp0 x3) Xy)
% Found (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x40)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)))) as proof of (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x3) Xy))
% Found (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x40)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x3) Xy)))
% Found x6:((Xr Xx) x2)
% Found x6 as proof of ((Xr Xx) x2)
% Found x10:=(x1 Xx):(forall (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))
% Found (x1 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found (x1 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))
% Found x7 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))
% Found x30:=(x3 Xx):(forall (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found x6:((Xr Xx) x0)
% Found x6 as proof of ((Xr Xx) x0)
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x3:((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x3:((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))->(((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (and_rect10 (fun (x3:((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((and_rect1 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x3:((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x3:(((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))->(((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))->P)))=> (((((and_rect ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) P) x3) x2)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x3:((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x3:(((ex a) (fun (Xz:a)=> ((and ((Xr Xx) Xz)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 Xz) Xy))))))->(((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))->P)))=> (((((and_rect ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) P) x3) x2)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x3:((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xy))))))) (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found x30:=(x3 Xx):(forall (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))
% Found x7 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))
% Found x6:((Xr Xx) x2)
% Found x6 as proof of ((Xr Xx) x2)
% Found x2:((Xr Xx) Xy)
% Instantiate: x3:=Xx:a
% Found x2 as proof of ((Xr x3) Xy)
% Found (x400 x2) as proof of ((Xp0 x3) Xy)
% Found ((x40 Xy) x2) as proof of ((Xp0 x3) Xy)
% Found (((x4 x3) Xy) x2) as proof of ((Xp0 x3) Xy)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)) as proof of ((Xp0 x3) Xy)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x3) Xy))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->((Xp0 x3) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2))) as proof of ((Xp0 x3) Xy)
% Found ((and_rect1 ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2))) as proof of ((Xp0 x3) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2))) as proof of ((Xp0 x3) Xy)
% Found (fun (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)))) as proof of ((Xp0 x3) Xy)
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)))) as proof of (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x3) Xy))
% Found (fun (Xp0:(a->(a->Prop))) (x00:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0)))) P) x4) x00)) ((Xp0 x3) Xy)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))=> (((x4 x3) Xy) x2)))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x3) Xy)))
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x10:=(x1 Xx):(forall (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))
% Found (x1 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found (x1 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found x30:=(x3 Xx):(forall (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))
% Found x7 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))
% Found x6:((Xr Xx) x0)
% Found x6 as proof of ((Xr Xx) x0)
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found ((x2 (fun (x5:a)=> (Xp x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found ((x2 (fun (x5:a)=> (Xp x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found x200:=(x20 Xy):(forall (Xz0:a), (((and ((Xp x0) Xy)) ((Xp Xy) Xz0))->((Xp x0) Xz0)))
% Found (x20 Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x2 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x2 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found x100:=(x10 Xy):(((Xr Xx) Xy)->((Xp Xx) Xy))
% Found (x10 Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x1 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x1 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found (fun (Xy:a)=> ((x1 Xx) Xy)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x30:=(x3 Xx):(forall (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found (x3 Xx) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))
% Found x400:=(x40 Xy):(forall (Xz0:a), (((and ((Xp x0) Xy)) ((Xp Xy) Xz0))->((Xp x0) Xz0)))
% Found (x40 Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found x300:=(x30 Xy):(((Xr Xx) Xy)->((Xp Xx) Xy))
% Found (x30 Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found (fun (Xy:a)=> ((x3 Xx) Xy)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x400:=(x40 Xy):(forall (Xz0:a), (((and ((Xp x0) Xy)) ((Xp Xy) Xz0))->((Xp x0) Xz0)))
% Found (x40 Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found x300:=(x30 Xy):(((Xr Xx) Xy)->((Xp Xx) Xy))
% Found (x30 Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found (fun (Xy:a)=> ((x3 Xx) Xy)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x4:((Xr Xx) x0)
% Found (fun (x5:((Xr Xy) x0))=> x4) as proof of ((Xr Xx) x0)
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xy) x0)->((Xr Xx) x0))
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xx) x0)->(((Xr Xy) x0)->((Xr Xx) x0)))
% Found (and_rect10 (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found ((and_rect1 ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (fun (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of ((Xr Xx) x0)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found x200:=(x20 Xy):(forall (Xz0:a), (((and ((Xp x0) Xy)) ((Xp Xy) Xz0))->((Xp x0) Xz0)))
% Found (x20 Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x2 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x2 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found x400:=(x40 Xy):(forall (Xz0:a), (((and ((Xp x0) Xy)) ((Xp Xy) Xz0))->((Xp x0) Xz0)))
% Found (x40 Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found x100:=(x10 Xy):(((Xr Xx) Xy)->((Xp Xx) Xy))
% Found (x10 Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x1 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x1 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found (fun (Xy:a)=> ((x1 Xx) Xy)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x300:=(x30 Xy):(((Xr Xx) Xy)->((Xp Xx) Xy))
% Found (x30 Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found (fun (Xy:a)=> ((x3 Xx) Xy)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x6:((Xr Xx) x2)
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6) as proof of ((Xr Xx) x2)
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((Xr Xx) x2))
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6) as proof of (((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((Xr Xx) x2)))
% Found (and_rect20 (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found ((and_rect2 ((Xr Xx) x2)) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((Xr Xx) x2)) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((Xr Xx) x2)) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x2000:=(x200 Xz):(((and ((Xp x0) Xy)) ((Xp Xy) Xz))->((Xp x0) Xz))
% Found (x200 Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found ((x20 Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x2 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x2 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xz:a)=> (((x2 x0) Xy) Xz)) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found x400:=(x40 Xy):(forall (Xz0:a), (((and ((Xp x0) Xy)) ((Xp Xy) Xz0))->((Xp x0) Xz0)))
% Found (x40 Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found ((x4 x0) Xy) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found x300:=(x30 Xy):(((Xr Xx) Xy)->((Xp Xx) Xy))
% Found (x30 Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found ((x3 Xx) Xy) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found (fun (Xy:a)=> ((x3 Xx) Xy)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x4000:=(x400 Xz):(((and ((Xp x0) Xy)) ((Xp Xy) Xz))->((Xp x0) Xz))
% Found (x400 Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found ((x40 Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xz:a)=> (((x4 x0) Xy) Xz)) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found conj100:=(conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))):((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found ((fun (B:Prop)=> ((conj1 B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) as proof of (((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (and_rect30 (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found ((and_rect3 ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))) as proof of (((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (and_rect20 (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found ((and_rect2 ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of (((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of (((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (and_rect10 (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found ((and_rect1 ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (forall (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (forall (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found x4:((Xr Xx) x0)
% Found (fun (x5:((Xr Xy) x0))=> x4) as proof of ((Xr Xx) x0)
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xy) x0)->((Xr Xx) x0))
% Found (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4) as proof of (((Xr Xx) x0)->(((Xr Xy) x0)->((Xr Xx) x0)))
% Found (and_rect10 (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found ((and_rect1 ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4)) as proof of ((Xr Xx) x0)
% Found (fun (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of ((Xr Xx) x0)
% Found (fun (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xr Xx) x0)) ((Xr Xy) x0)))=> (((fun (P:Type) (x4:(((Xr Xx) x0)->(((Xr Xy) x0)->P)))=> (((((and_rect ((Xr Xx) x0)) ((Xr Xy) x0)) P) x4) x3)) ((Xr Xx) x0)) (fun (x4:((Xr Xx) x0)) (x5:((Xr Xy) x0))=> x4))) as proof of (forall (Xx:a) (Xy:a), (a->(((and ((Xr Xx) x0)) ((Xr Xy) x0))->((Xr Xx) x0))))
% Found x6:((Xr Xx) x0)
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6) as proof of ((Xr Xx) x0)
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((Xr Xx) x0))
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6) as proof of (((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((Xr Xx) x0)))
% Found (and_rect20 (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found ((and_rect2 ((Xr Xx) x0)) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((Xr Xx) x0)) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((Xr Xx) x0)) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found x4000:=(x400 Xz):(((and ((Xp x0) Xy)) ((Xp Xy) Xz))->((Xp x0) Xz))
% Found (x400 Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found ((x40 Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xz:a)=> (((x4 x0) Xy) Xz)) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found x6:((Xr Xx) x2)
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6) as proof of ((Xr Xx) x2)
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((Xr Xx) x2))
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6) as proof of (((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((Xr Xx) x2)))
% Found (and_rect20 (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found ((and_rect2 ((Xr Xx) x2)) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((Xr Xx) x2)) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((Xr Xx) x2)) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> x6)) as proof of ((Xr Xx) x2)
% Found conj100:=(conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))):((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found ((fun (B:Prop)=> ((conj1 B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) as proof of (((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (and_rect30 (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found ((and_rect3 ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))) as proof of (((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (and_rect20 (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found ((and_rect2 ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of (((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of (((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (and_rect10 (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found ((and_rect1 ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (forall (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (forall (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found x2000:=(x200 Xz):(((and ((Xp x0) Xy)) ((Xp Xy) Xz))->((Xp x0) Xz))
% Found (x200 Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found ((x20 Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x2 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x2 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xz:a)=> (((x2 x0) Xy) Xz)) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found x4000:=(x400 Xz):(((and ((Xp x0) Xy)) ((Xp Xy) Xz))->((Xp x0) Xz))
% Found (x400 Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found ((x40 Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xz:a)=> (((x4 x0) Xy) Xz)) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found conj100:=(conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))):((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found ((fun (B:Prop)=> ((conj1 B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) as proof of (((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (and_rect30 (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found ((and_rect3 ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))) as proof of (((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (and_rect20 (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found ((and_rect2 ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of (((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))) as proof of (((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (and_rect10 (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found ((and_rect1 ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))
% Found (fun (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (forall (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (forall (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))->(((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) P) x4) x3)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x4:((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) (x5:((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))->P)))=> (((((and_rect ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy)))) P) x6) x4)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x6:((Xr Xx) x2)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x2)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))->P)))=> (((((and_rect ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz)))) P) x8) x5)) ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))) (fun (x8:((Xr Xy) x2))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x2)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xy))))) ((and ((Xr Xy) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x2) Xz)))))->((and ((Xr Xx) x2)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x2) Xz))))))
% Found x4000:=(x400 Xz):(((and ((Xp x0) Xy)) ((Xp Xy) Xz))->((Xp x0) Xz))
% Found (x400 Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found ((x40 Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (((x4 x0) Xy) Xz) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xz:a)=> (((x4 x0) Xy) Xz)) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found x6:((Xr Xx) x0)
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6) as proof of ((Xr Xx) x0)
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((Xr Xx) x0))
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6) as proof of (((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((Xr Xx) x0)))
% Found (and_rect20 (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found ((and_rect2 ((Xr Xx) x0)) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((Xr Xx) x0)) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((Xr Xx) x0)) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> x6)) as proof of ((Xr Xx) x0)
% Found x5:((Xp x0) Xz)
% Found (fun (x5:((Xp x0) Xz))=> x5) as proof of ((Xp x0) Xz)
% Found (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect10 (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5)) as proof of ((Xp x0) Xz)
% Found ((and_rect1 ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5)) as proof of ((Xp x0) Xz)
% Found (fun (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found conj100:=(conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))):((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (conj10 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found ((fun (B:Prop)=> ((conj1 B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) as proof of (((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (and_rect30 (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found ((and_rect3 ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))) as proof of (((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (and_rect20 (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found ((and_rect2 ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of (((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))) as proof of (((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (and_rect10 (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found ((and_rect1 ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))
% Found (fun (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (forall (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (forall (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz))))))=> (((fun (P:Type) (x4:(((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))->(((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))->P)))=> (((((and_rect ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) P) x4) x3)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x4:((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) (x5:((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))))=> (((fun (P:Type) (x6:(((Xr Xx) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))->P)))=> (((((and_rect ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy)))) P) x6) x4)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x6:((Xr Xx) x0)) (x7:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))=> (((fun (P:Type) (x8:(((Xr Xy) x0)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))->P)))=> (((((and_rect ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz)))) P) x8) x5)) ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))) (fun (x8:((Xr Xy) x0))=> ((fun (B:Prop)=> (((conj ((Xr Xx) x0)) B) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((and ((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xy))))) ((and ((Xr Xy) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp0 Xx) Xy0)))) (forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp0 Xx) Xy0)) ((Xp0 Xy0) Xz0))->((Xp0 Xx) Xz0))))->((Xp0 x0) Xz)))))->((and ((Xr Xx) x0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz0))->((Xp0 Xx0) Xz0))))->((Xp0 x0) Xz))))))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x3 as proof of ((Xr x0) Xy)
% Found (x400 x3) as proof of ((Xp x0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp x0) Xy)
% Found (((x4 x0) Xy) x3) as proof of ((Xp x0) Xy)
% Found (fun (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((Xp x0) Xy)
% Found (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xy))
% Found (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp x0) Xy)
% Found ((and_rect1 ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp x0) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))) P) x4) x00)) ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp x0) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> (((fun (P:Type) (x4:((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))) P) x4) x00)) ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> (((fun (P:Type) (x4:((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))) P) x4) x00)) ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x5:((Xp x0) Xz)
% Found (fun (x5:((Xp x0) Xz))=> x5) as proof of ((Xp x0) Xz)
% Found (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect10 (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5)) as proof of ((Xp x0) Xz)
% Found ((and_rect1 ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5)) as proof of ((Xp x0) Xz)
% Found (fun (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x4:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((Xp x0) Xy)) (x5:((Xp x0) Xz))=> x5))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr x0) Xy))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr x0) Xy))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x3 as proof of ((Xr x0) Xy)
% Found (x400 x3) as proof of ((Xp x0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp x0) Xy)
% Found (((x4 x0) Xy) x3) as proof of ((Xp x0) Xy)
% Found (fun (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((Xp x0) Xy)
% Found (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xy))
% Found (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)) as proof of ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xy)))
% Found (and_rect10 (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp x0) Xy)
% Found ((and_rect1 ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp x0) Xy)
% Found (((fun (P:Type) (x4:((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))) P) x4) x00)) ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3))) as proof of ((Xp x0) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> (((fun (P:Type) (x4:((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))) P) x4) x00)) ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> (((fun (P:Type) (x4:((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))) (forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))) P) x4) x00)) ((Xp x0) Xy)) (fun (x4:(forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))) (x5:(forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0))))=> (((x4 x0) Xy) x3)))) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr x0) Xy))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))))) as proof of ((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xt)))
% Found ((x2 (fun (x5:a) (x40:a)=> ((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) x40))))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))))) as proof of ((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xt)))
% Found ((x2 (fun (x5:a) (x40:a)=> ((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) x40))))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))))) as proof of ((forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp Xx) Xy)))->((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xt)))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr x0) Xy))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr x0) Xy))
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (ex_ind00 (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((ex_ind0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Prop) (x5:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x5) x4)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Prop) (x5:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x5) x4)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (ex_ind00 (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((ex_ind0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Prop) (x5:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x5) x4)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> (((fun (P:Prop) (x5:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x5) x4)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x4:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> (((fun (P:Prop) (x5:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x5) x4)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of (((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr x0) Xy))
% Found False_rect00:=(False_rect0 ((Xr Xx) x3)):((Xr Xx) x3)
% Found (False_rect0 ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x5 as proof of ((Xr x0) Xy)
% Found (x100 x5) as proof of ((Xp x0) Xy)
% Found ((x10 Xy) x5) as proof of ((Xp x0) Xy)
% Found (((x1 x0) Xy) x5) as proof of ((Xp x0) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> (((x1 x0) Xy) x5)) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> (((x1 x0) Xy) x5)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x5 as proof of ((Xr x0) Xy)
% Found (x300 x5) as proof of ((Xp x0) Xy)
% Found ((x30 Xy) x5) as proof of ((Xp x0) Xy)
% Found (((x3 x0) Xy) x5) as proof of ((Xp x0) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))) as proof of ((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xt))
% Found ((x2 (fun (x6:a) (x50:a)=> ((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) x50)))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))) as proof of ((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xt))
% Found ((x2 (fun (x6:a) (x50:a)=> ((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) x50)))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))) (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))))) as proof of ((forall (Xx:a) (Xy:a) (Xz0:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xt))
% Found x3:((Xr Xx) Xy)
% Found (fun (x3:((Xr Xx) Xy))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x5 as proof of ((Xr x0) Xy)
% Found (x300 x5) as proof of ((Xp x0) Xy)
% Found ((x30 Xy) x5) as proof of ((Xp x0) Xy)
% Found (((x3 x0) Xy) x5) as proof of ((Xp x0) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x4:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x4 as proof of ((Xr x0) Xy)
% Found (x300 x4) as proof of ((Xp x0) Xy)
% Found ((x30 Xy) x4) as proof of ((Xp x0) Xy)
% Found (((x3 x0) Xy) x4) as proof of ((Xp x0) Xy)
% Found (fun (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x3 x0) Xy) x4)) as proof of ((Xp x0) Xy)
% Found (fun (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x3 x0) Xy) x4)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))
% Found (fun (Xy:a) (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x3 x0) Xy) x4)) as proof of (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x3 as proof of ((Xr x0) Xy)
% Found (x3000 x3) as proof of ((Xp x0) Xy)
% Found ((x300 Xy) x3) as proof of ((Xp x0) Xy)
% Found (((x30 x0) Xy) x3) as proof of ((Xp x0) Xy)
% Found (fun (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of ((Xp x0) Xy)
% Found (fun (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))
% Found (fun (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))
% Found (fun (Xy:a) (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))
% Found x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))
% Instantiate: x9:=x5:a
% Found x8 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x9) Xz)))
% Found x3:((Xr Xx) Xy)
% Instantiate: Xy0:=Xx:a
% Found x3 as proof of ((Xr Xy0) Xy)
% Found (x400 x3) as proof of ((Xp0 Xy0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found x7:((Xr Xx) x5)
% Instantiate: x9:=x5:a
% Found x7 as proof of ((Xr Xx) x9)
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x5 as proof of ((Xr x0) Xy)
% Found (x100 x5) as proof of ((Xp x0) Xy)
% Found ((x10 Xy) x5) as proof of ((Xp x0) Xy)
% Found (((x1 x0) Xy) x5) as proof of ((Xp x0) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> (((x1 x0) Xy) x5)) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> (((x1 x0) Xy) x5)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found (x40 ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found ((x4 (fun (x7:a)=> (Xp x0))) ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found ((x4 (fun (x7:a)=> (Xp x0))) ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x5 as proof of ((Xr x0) Xy)
% Found (x300 x5) as proof of ((Xp x0) Xy)
% Found ((x30 Xy) x5) as proof of ((Xp x0) Xy)
% Found (((x3 x0) Xy) x5) as proof of ((Xp x0) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found ((x2 (fun (x7:a)=> (Xp x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found ((x2 (fun (x7:a)=> (Xp x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xp x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))))) as proof of ((Xp x0) Xt)
% Found x4:((Xr Xx) Xy)
% Found (fun (x4:((Xr Xx) Xy))=> x4) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x4:((Xr Xx) Xy))=> x4) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x4:((Xr Xx) Xy))=> x4) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x4:((Xr Xx) Xy))=> x4) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found False_rect00:=(False_rect0 ((Xp0 x3) Xz)):((Xp0 x3) Xz)
% Found (False_rect0 ((Xp0 x3) Xz)) as proof of ((Xp0 x3) Xz)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz)) as proof of ((Xp0 x3) Xz)
% Found (fun (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz))) as proof of ((Xp0 x3) Xz)
% Found (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz))) as proof of (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))
% Found (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))
% Found ((conj10 ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz)))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (((conj1 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))) ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz)))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found ((((conj ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))) ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz)))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found ((((conj ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))) ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x3) Xz)))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found x4:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x4 as proof of ((Xr x0) Xy)
% Found (x300 x4) as proof of ((Xp x0) Xy)
% Found ((x30 Xy) x4) as proof of ((Xp x0) Xy)
% Found (((x3 x0) Xy) x4) as proof of ((Xp x0) Xy)
% Found (fun (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x3 x0) Xy) x4)) as proof of ((Xp x0) Xy)
% Found (fun (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x3 x0) Xy) x4)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))
% Found (fun (Xy:a) (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x3 x0) Xy) x4)) as proof of (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))
% Found x5:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x5 as proof of ((Xr x0) Xy)
% Found (x300 x5) as proof of ((Xp x0) Xy)
% Found ((x30 Xy) x5) as proof of ((Xp x0) Xy)
% Found (((x3 x0) Xy) x5) as proof of ((Xp x0) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of ((Xp x0) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> (((x3 x0) Xy) x5)) as proof of (((Xr Xx) Xy)->((Xp x0) Xy))
% Found x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))
% Instantiate: x3:=x6:a
% Found x9 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))
% Found x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))
% Instantiate: x7:=x5:a
% Found x9 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x7) Xz)))
% Found x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))
% Instantiate: x5:=x6:a
% Found x9 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))
% Found x3:((Xr Xx) Xy)
% Instantiate: Xy0:=Xx:a
% Found x3 as proof of ((Xr Xy0) Xy)
% Found (x400 x3) as proof of ((Xp0 Xy0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found x8:((Xr Xx) x6)
% Instantiate: x3:=x6:a
% Found x8 as proof of ((Xr Xx) x3)
% Found x8:((Xr Xx) x6)
% Instantiate: x5:=x6:a
% Found x8 as proof of ((Xr Xx) x5)
% Found x8:((Xr Xx) x5)
% Instantiate: x7:=x5:a
% Found x8 as proof of ((Xr Xx) x7)
% Found x3:((Xr Xx) Xy)
% Instantiate: x0:=Xx:a
% Found x3 as proof of ((Xr x0) Xy)
% Found (x3000 x3) as proof of ((Xp x0) Xy)
% Found ((x300 Xy) x3) as proof of ((Xp x0) Xy)
% Found (((x30 x0) Xy) x3) as proof of ((Xp x0) Xy)
% Found (fun (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of ((Xp x0) Xy)
% Found (fun (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))
% Found (fun (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))
% Found (fun (Xy:a) (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> (((x30 x0) Xy) x3)) as proof of (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))))
% Found x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))
% Instantiate: x9:=x5:a
% Found x8 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x9) Xz)))
% Found x7:((Xr Xx) x5)
% Instantiate: x9:=x5:a
% Found x7 as proof of ((Xr Xx) x9)
% Found x5:((Xr Xx) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x3:((Xr Xx) Xy)
% Instantiate: Xy0:=Xx:a
% Found x3 as proof of ((Xr Xy0) Xy)
% Found (x400 x3) as proof of ((Xp0 Xy0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found x5:((Xr Xx) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x5:((Xr Xx) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))
% Instantiate: x3:=x6:a
% Found x9 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))
% Found x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))
% Instantiate: x7:=x5:a
% Found x9 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x7) Xz)))
% Found x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))
% Instantiate: x5:=x6:a
% Found x9 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))
% Found x8:((Xr Xx) x6)
% Instantiate: x3:=x6:a
% Found x8 as proof of ((Xr Xx) x3)
% Found x8:((Xr Xx) x6)
% Instantiate: x5:=x6:a
% Found x8 as proof of ((Xr Xx) x5)
% Found x8:((Xr Xx) x5)
% Instantiate: x7:=x5:a
% Found x8 as proof of ((Xr Xx) x7)
% Found x5:((Xr Xx) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x4:((Xr Xx) Xy)
% Found (fun (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x4) as proof of ((Xr Xx) Xy)
% Found (fun (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x4) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy))
% Found (fun (Xy:a) (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x4) as proof of (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x4) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy))))
% Found (fun (Xx:a) (Xy:a) (x4:((Xr Xx) Xy)) (x40:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x4) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy))))
% Found x3:((Xr Xx) Xy)
% Instantiate: Xy0:=Xx:a
% Found x3 as proof of ((Xr Xy0) Xy)
% Found (x400 x3) as proof of ((Xp0 Xy0) Xy)
% Found ((x40 Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found (((x4 Xy0) Xy) x3) as proof of ((Xp0 Xy0) Xy)
% Found x3:((Xr Xx) Xy)
% Found (fun (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x3) as proof of ((Xr Xx) Xy)
% Found (fun (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x3) as proof of ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy))
% Found (fun (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x3) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy)))
% Found (fun (Xy:a) (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x3) as proof of (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy))))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x3) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy)))))
% Found (fun (Xx:a) (Xy:a) (x3:((Xr Xx) Xy)) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x400:(forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))=> x3) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xr Xx) Xy)))))
% Found x7:((Xp x0) Xz)
% Found (fun (x7:((Xp x0) Xz))=> x7) as proof of ((Xp x0) Xz)
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect20 (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found x7:((Xp x0) Xz)
% Found (fun (x7:((Xp x0) Xz))=> x7) as proof of ((Xp x0) Xz)
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect20 (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found x7:((Xp x0) Xz)
% Found (fun (x7:((Xp x0) Xz))=> x7) as proof of ((Xp x0) Xz)
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect20 (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found x8:((Xr Xx) x6)
% Instantiate: x3:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x3)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found ((and_rect2 ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found x8:((Xr Xx) x5)
% Instantiate: x7:=x5:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8) as proof of ((Xr Xx) x7)
% Found (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((Xr Xx) x7))
% Found (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8) as proof of (((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((Xr Xx) x7)))
% Found (and_rect20 (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found ((and_rect2 ((Xr Xx) x7)) (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found (((fun (P:Type) (x8:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x8) x6)) ((Xr Xx) x7)) (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found (((fun (P:Type) (x8:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x8) x6)) ((Xr Xx) x7)) (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found x8:((Xr Xx) x6)
% Instantiate: x5:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x5)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found ((and_rect2 ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found x7:((Xp x0) Xz)
% Found (fun (x7:((Xp x0) Xz))=> x7) as proof of ((Xp x0) Xz)
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect20 (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found x7:((Xp x0) Xz)
% Found (fun (x7:((Xp x0) Xz))=> x7) as proof of ((Xp x0) Xz)
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect20 (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found (x40 ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found ((x4 (fun (x7:a)=> (Xr x0))) ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found ((x4 (fun (x7:a)=> (Xr x0))) ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found (x20 ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found ((x2 (fun (x7:a)=> (Xr x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found ((x2 (fun (x7:a)=> (Xr x0))) ((fun (P:Type)=> ((False_rect P) x10)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found x8:((Xr Xx) x6)
% Instantiate: x3:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x3)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found ((and_rect2 ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found x8:((Xr Xx) x5)
% Instantiate: x7:=x5:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8) as proof of ((Xr Xx) x7)
% Found (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((Xr Xx) x7))
% Found (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8) as proof of (((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((Xr Xx) x7)))
% Found (and_rect20 (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found ((and_rect2 ((Xr Xx) x7)) (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found (((fun (P:Type) (x8:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x8) x6)) ((Xr Xx) x7)) (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found (((fun (P:Type) (x8:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x8) x6)) ((Xr Xx) x7)) (fun (x8:((Xr Xx) x5)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> x8)) as proof of ((Xr Xx) x7)
% Found x7:((Xp x0) Xz)
% Found (fun (x7:((Xp x0) Xz))=> x7) as proof of ((Xp x0) Xz)
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xz)->((Xp x0) Xz))
% Found (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7) as proof of (((Xp x0) Xy)->(((Xp x0) Xz)->((Xp x0) Xz)))
% Found (and_rect20 (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of ((Xp x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xp x0) Xy)) ((Xp x0) Xz)))=> (((fun (P:Type) (x6:(((Xp x0) Xy)->(((Xp x0) Xz)->P)))=> (((((and_rect ((Xp x0) Xy)) ((Xp x0) Xz)) P) x6) x5)) ((Xp x0) Xz)) (fun (x6:((Xp x0) Xy)) (x7:((Xp x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xp x0) Xy)) ((Xp x0) Xz))->((Xp x0) Xz))))
% Found x8:((Xr Xx) x6)
% Instantiate: x5:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x5)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found ((and_rect2 ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found False_rect00:=(False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))):((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found (False_rect0 ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))) as proof of ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))))
% Found (x40 ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found ((x4 (fun (x7:a)=> (Xr x0))) ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found ((x4 (fun (x7:a)=> (Xr x0))) ((fun (P:Type)=> ((False_rect P) x30)) ((and (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr x0) Xy)))) (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))))) as proof of ((Xr x0) Xt)
% Found x5:((Xr Xx) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x5:((Xr Xx) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x60:=(x6 x40):((Xp x0) Xz)
% Found (x6 x40) as proof of ((Xp x0) Xz)
% Found (fun (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)) as proof of (((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)) as proof of (((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->((Xp x0) Xz)))
% Found (and_rect20 (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40))) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40))) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40))) as proof of ((Xp x0) Xz)
% Found (fun (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of ((Xp x0) Xz)
% Found (fun (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of ((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))
% Found (fun (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))
% Found (fun (Xy:a) (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (forall (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (and_rect20 (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((and_rect2 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (and_rect20 (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((and_rect2 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of (((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (and_rect20 (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((and_rect2 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found False_rect00:=(False_rect0 ((Xr Xx) x5)):((Xr Xx) x5)
% Found (False_rect0 ((Xr Xx) x5)) as proof of ((Xr Xx) x5)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x5)) as proof of ((Xr Xx) x5)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x5)) as proof of ((Xr Xx) x5)
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (and_rect20 (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((and_rect2 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))))=> (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))))=> (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of (((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found x5:((Xr Xx) Xy)
% Found (fun (x5:((Xr Xx) Xy))=> x5) as proof of ((Xr Xx) Xy)
% Found (fun (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (((Xr Xx) Xy)->((Xr Xx) Xy))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found (fun (Xx:a) (Xy:a) (x5:((Xr Xx) Xy))=> x5) as proof of (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xx) Xy)))
% Found x8:((Xr Xx) x6)
% Instantiate: x3:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x3)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found ((and_rect2 ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (fun (x7:((and ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))))=> (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8))) as proof of ((Xr Xx) x3)
% Found x8:((Xr Xx) x6)
% Instantiate: x5:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x5)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found ((and_rect2 ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (fun (x7:((and ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))))=> (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8))) as proof of ((Xr Xx) x5)
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (and_rect20 (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((and_rect2 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of (((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x5:a) (x6:((and ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))))=> (((fun (P:Type) (x7:(((Xr Xy) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))->P)))=> (((((and_rect ((Xr Xy) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xy) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of (forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found False_rect00:=(False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))):((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (False_rect0 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))) as proof of (((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found (and_rect20 (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((and_rect2 ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x6:((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))))=> (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found (fun (x5:a) (x6:((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))))=> (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of (((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))
% Found (fun (x5:a) (x6:((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))))=> (((fun (P:Type) (x7:(((Xr Xx) x5)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))->P)))=> (((((and_rect ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy)))) P) x7) x6)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))) (fun (x7:((Xr Xx) x5)) (x8:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xy))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))))) as proof of (forall (x:a), (((and ((Xr Xx) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xy))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))))
% Found False_rect00:=(False_rect0 ((Xr Xx) x3)):((Xr Xx) x3)
% Found (False_rect0 ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found x60:=(x6 x40):((Xp x0) Xz)
% Found (x6 x40) as proof of ((Xp x0) Xz)
% Found (fun (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)) as proof of ((Xp x0) Xz)
% Found (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)) as proof of (((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->((Xp x0) Xz))
% Found (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)) as proof of (((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->((Xp x0) Xz)))
% Found (and_rect20 (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40))) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40))) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40))) as proof of ((Xp x0) Xz)
% Found (fun (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of ((Xp x0) Xz)
% Found (fun (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of ((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))
% Found (fun (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))
% Found (fun (Xy:a) (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (forall (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x4:((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) (x40:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x5:(((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))->(((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))) P) x5) x4)) ((Xp x0) Xz)) (fun (x5:((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) (x6:((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))=> (x6 x40)))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy))) ((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))
% Found False_rect00:=(False_rect0 ((Xr Xx) x3)):((Xr Xx) x3)
% Found (False_rect0 ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x3)) as proof of ((Xr Xx) x3)
% Found x8:((Xr Xx) x6)
% Instantiate: x3:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x3)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x3)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found ((and_rect2 ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x3)
% Found (fun (x7:((and ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))))=> (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x3)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8))) as proof of ((Xr Xx) x3)
% Found x8:((Xr Xx) x6)
% Instantiate: x5:=x6:a
% Found (fun (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((Xr Xx) x5)
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of ((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5))
% Found (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8) as proof of (((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->((Xr Xx) x5)))
% Found (and_rect20 (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found ((and_rect2 ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8)) as proof of ((Xr Xx) x5)
% Found (fun (x7:((and ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))))=> (((fun (P:Type) (x8:(((Xr Xx) x6)->((forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))->P)))=> (((((and_rect ((Xr Xx) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy)))) P) x8) x7)) ((Xr Xx) x5)) (fun (x8:((Xr Xx) x6)) (x9:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xy))))=> x8))) as proof of ((Xr Xx) x5)
% Found False_rect00:=(False_rect0 ((Xp0 x5) Xz)):((Xp0 x5) Xz)
% Found (False_rect0 ((Xp0 x5) Xz)) as proof of ((Xp0 x5) Xz)
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz)) as proof of ((Xp0 x5) Xz)
% Found (fun (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz))) as proof of ((Xp0 x5) Xz)
% Found (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz))) as proof of (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))
% Found (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz))) as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))
% Found ((conj10 ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x5))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz)))) as proof of ((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))
% Found (((conj1 (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x5))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz)))) as proof of ((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))
% Found ((((conj ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x5))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz)))) as proof of ((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))
% Found ((((conj ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz)))) ((fun (P:Type)=> ((False_rect P) x00)) ((Xr Xx) x5))) (fun (Xp0:(a->(a->Prop))) (x40:((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((Xp0 x5) Xz)))) as proof of ((and ((Xr Xx) x5)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x5) Xz))))
% Found False_rect00:=(False_rect0 ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))):((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (False_rect0 ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (fun (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))) as proof of (((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz))))->((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))
% Found (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))) as proof of (forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))
% Found (ex_ind00 (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found ((ex_ind0 ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (((fun (P:Prop) (x6:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x6) x5)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (((fun (P:Prop) (x6:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x6) x5)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found False_rect00:=(False_rect0 ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))):((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (False_rect0 ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (fun (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))) as proof of (((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz))))->((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))
% Found (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))) as proof of (forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))
% Found (ex_ind00 (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found ((ex_ind0 ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (((fun (P:Prop) (x6:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x6) x5)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (fun (x5:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> (((fun (P:Prop) (x6:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x6) x5)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))))) as proof of ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))
% Found (fun (x5:((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))))=> (((fun (P:Prop) (x6:(forall (x:a), (((and ((Xr Xy) x)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x) Xz))))->P)))=> (((((ex_ind a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz)))))) P) x6) x5)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz))))) (fun (x6:a) (x7:((and ((Xr Xy) x6)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x6) Xz)))))=> ((fun (P:Type)=> ((False_rect P) x00)) ((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))))) as proof of (((ex a) (fun (Xz0:a)=> ((and ((Xr Xy) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))->((and ((Xr Xx) x3)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x3) Xz)))))
% Found x500:=(x50 x400):((Xp x0) Xz)
% Found (x50 x400) as proof of ((Xp x0) Xz)
% Found ((x5 x30) x400) as proof of ((Xp x0) Xz)
% Found (fun (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)) as proof of ((Xp x0) Xz)
% Found (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)) as proof of (((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((Xp x0) Xz))
% Found (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)) as proof of (((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->((Xp x0) Xz)))
% Found (and_rect20 (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400))) as proof of ((Xp x0) Xz)
% Found ((and_rect2 ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400))) as proof of ((Xp x0) Xz)
% Found (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400))) as proof of ((Xp x0) Xz)
% Found (fun (x400:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)))) as proof of ((Xp x0) Xz)
% Found (fun (x30:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))) (x400:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)))) as proof of ((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))
% Found (fun (x3:((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))) (x30:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))) (x400:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)))) as proof of ((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))
% Found (fun (Xz:a) (x3:((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))) (x30:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))) (x400:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)))) as proof of (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))
% Found (fun (Xy:a) (Xz:a) (x3:((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))) (x30:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))) (x400:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)))) as proof of (forall (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))) (x30:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))) (x400:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)))) as proof of (forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz)))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x3:((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))) (x30:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))) (x400:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0))))=> (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))->(((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz)))) P) x4) x3)) ((Xp x0) Xz)) (fun (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) (x5:((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))=> ((x5 x30) x400)))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xy)))) ((forall (Xx:a) (Xy0:a), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))->((forall (Xx:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx) Xz0)))->((Xp x0) Xz))))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp Xx0) Xy)))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz0))->((Xp Xx0) Xz0)))->((Xp x0) Xz))))))
% Found x7:((Xr x0) Xz)
% Found (fun (x7:((Xr x0) Xz))=> x7) as proof of ((Xr x0) Xz)
% Found (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7) as proof of (((Xr x0) Xz)->((Xr x0) Xz))
% Found (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7) as proof of (((Xr x0) Xy)->(((Xr x0) Xz)->((Xr x0) Xz)))
% Found (and_rect20 (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7)) as proof of ((Xr x0) Xz)
% Found ((and_rect2 ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7)) as proof of ((Xr x0) Xz)
% Found (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7)) as proof of ((Xr x0) Xz)
% Found (fun (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of ((Xr x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))
% Found x7:((Xr x0) Xz)
% Found (fun (x7:((Xr x0) Xz))=> x7) as proof of ((Xr x0) Xz)
% Found (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7) as proof of (((Xr x0) Xz)->((Xr x0) Xz))
% Found (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7) as proof of (((Xr x0) Xy)->(((Xr x0) Xz)->((Xr x0) Xz)))
% Found (and_rect20 (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7)) as proof of ((Xr x0) Xz)
% Found ((and_rect2 ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7)) as proof of ((Xr x0) Xz)
% Found (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7)) as proof of ((Xr x0) Xz)
% Found (fun (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of ((Xr x0) Xz)
% Found (fun (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))
% Found (fun (Xy:a) (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (forall (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz)))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x5:((and ((Xr x0) Xy)) ((Xr x0) Xz)))=> (((fun (P:Type) (x6:(((Xr x0) Xy)->(((Xr x0) Xz)->P)))=> (((((and_rect ((Xr x0) Xy)) ((Xr x0) Xz)) P) x6) x5)) ((Xr x0) Xz)) (fun (x6:((Xr x0) Xy)) (x7:((Xr x0) Xz))=> x7))) as proof of (a->(forall (Xy:a) (Xz:a), (((and ((Xr x0) Xy)) ((Xr x0) Xz))->((Xr x0) Xz))))
% Found False_rect00:=(False_rect0 ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))):((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))
% Found (False_rect0 ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00))))))))))
% Found (x80 ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00)))))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((x8 (fun (x11:a) (x90:a)=> ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp00 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp00 Xx0) Xy0)) ((Xp00 Xy0) Xz00))->((Xp00 Xx0) Xz00))))->((Xp00 Xz0) x90)))))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00)))))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((x8 (fun (x11:a) (x90:a)=> ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp00 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp00 Xx0) Xy0)) ((Xp00 Xy0) Xz00))->((Xp00 Xx0) Xz00))))->((Xp00 Xz0) x90)))))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))))) (a->(forall (Xy0:a) (Xz00:a), (((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xy0))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz00)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz00)))))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found x11:(forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp0 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp0 Xx0) Xy0)) ((Xp0 Xy0) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x7) Xz)))
% Instantiate: x12:=x7:a
% Found x11 as proof of (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 x12) Xz)))
% Found x9:((Xr Xx) x7)
% Instantiate: x12:=x7:a
% Found x9 as proof of ((Xr Xx) x12)
% Found False_rect00:=(False_rect0 ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))):((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))
% Found (False_rect0 ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))
% Found ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz)))))))))))
% Found (x80 ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz))))))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((x8 (fun (x11:a) (x90:a)=> ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp00 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp00 Xx0) Xy0)) ((Xp00 Xy0) Xz00))->((Xp00 Xx0) Xz00))))->((Xp00 Xz0) Xz)))))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a) (Xz000:a), (((and ((Xp00 Xx0) Xy00)) ((Xp00 Xy00) Xz000))->((Xp00 Xx0) Xz000))))->((Xp00 Xz0) Xz)))))))->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp00 Xx00) Xy0)))) (forall (Xx00:a) (Xy0:a) (Xz000:a), (((and ((Xp00 Xx00) Xy0)) ((Xp00 Xy0) Xz000))->((Xp00 Xx00) Xz000))))->((Xp00 Xz0) Xz))))))))))))) as proof of ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp0:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xp0 Xx0) Xy)))) (forall (Xx0:a) (Xy:a) (Xz00:a), (((and ((Xp0 Xx0) Xy)) ((Xp0 Xy) Xz00))->((Xp0 Xx0) Xz00))))->((Xp0 Xz0) Xz))))))
% Found ((x8 (fun (x11:a) (x90:a)=> ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp00 Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz00:a), (((and ((Xp00 Xx0) Xy0)) ((Xp00 Xy0) Xz00))->((Xp00 Xx0) Xz00))))->((Xp00 Xz0) Xz)))))))) ((fun (P:Type)=> ((False_rect P) x00)) ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))))) (a->(a->(a->(((and ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp00 Xx00) Xy00)))) (forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp00 Xx00) Xy00)) ((Xp00 Xy00) Xz00))->((Xp00 Xx00) Xz00))))->((Xp00 Xz0) Xz))))))) ((ex a) (fun (Xz0:a)=> ((and ((Xr Xx) Xz0)) (forall (Xp00:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp00 Xx0) Xy00)))) (f
% EOF
%------------------------------------------------------------------------------