%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : GRA027^1 : TPTP v6.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n185.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 13:22:12 EDT 2014

% Result   : Timeout 300.00s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRA027^1 : TPTP v6.1.0. Released v3.6.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n185.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:37:11 CDT 2014
% % CPUTime  : 300.00 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula ((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False)))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1))))))) of role conjecture named ramsey_l_3_3_4
% Conjecture to prove = ((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False)))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1))))))):Prop
% We need to prove ['((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False)))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1)))))))']
% Trying to prove ((ex ((Prop->Prop)->((Prop->Prop)->Prop))) (fun (G:((Prop->Prop)->((Prop->Prop)->Prop)))=> ((and ((and (forall (Xx:(Prop->Prop)) (Xy:(Prop->Prop)), (((G Xx) Xy)->((G Xy) Xx)))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((G Xx1) Xx0)->False)) (((G Xx2) Xx0)->False))) (((G Xx2) Xx1)->False)))))) (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or ((G Xx1) Xx0)) ((G Xx2) Xx0))) ((G Xx2) Xx1)))))))
% Found x03:(Xp1 Xx1)
% Instantiate: x:=(fun (x2:(Prop->Prop)) (x10:(Prop->Prop))=> (Xp1 x2)):((Prop->Prop)->((Prop->Prop)->Prop))
% Found (fun (x03:(Xp1 Xx1))=> x03) as proof of ((x Xx1) Xx0)
% Found (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03) as proof of ((Xp1 Xx1)->((x Xx1) Xx0))
% Found (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03) as proof of (((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->((x Xx1) Xx0)))
% Found (and_rect10 (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found ((and_rect1 ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found (fun (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of ((x Xx1) Xx0)
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of (((Xp1 Xx2)->False)->((x Xx1) Xx0))
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of (((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->((x Xx1) Xx0)))
% Found (and_rect00 (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found ((and_rect0 ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found (or_introl10 (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found ((or_introl1 ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (or_introl00 (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found ((or_introl0 ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (fun (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found x03:(Xp1 Xx1)
% Instantiate: x:=(fun (x2:(Prop->Prop)) (x10:(Prop->Prop))=> (Xp1 x2)):((Prop->Prop)->((Prop->Prop)->Prop))
% Found (fun (x03:(Xp1 Xx1))=> x03) as proof of ((x Xx1) Xx0)
% Found (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03) as proof of ((Xp1 Xx1)->((x Xx1) Xx0))
% Found (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03) as proof of (((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->((x Xx1) Xx0)))
% Found (and_rect10 (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found ((and_rect1 ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found (or_introl10 (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found ((or_introl1 ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (or_introl00 (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found ((or_introl0 ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (fun (x01:((Xp1 Xx2)->False))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of (((Xp1 Xx2)->False)->((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)))
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of (((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))))
% Found (and_rect00 (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found ((and_rect0 ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (fun (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_introl ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1)) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found x01:((Xp1 Xx2)->False)
% Instantiate: x:=(fun (x2:(Prop->Prop)) (x10:(Prop->Prop))=> (Xp1 x2)):((Prop->Prop)->((Prop->Prop)->Prop))
% Found x01 as proof of (((x Xx2) Xx1)->False)
% Found (or_intror00 x01) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found ((or_intror0 (((x Xx2) Xx1)->False)) x01) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (fun (x01:((Xp1 Xx2)->False))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01)) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01)) as proof of (((Xp1 Xx2)->False)->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)))
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01)) as proof of (((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))))
% Found (and_rect00 (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found ((and_rect0 ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (fun (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) x01)))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found x0000:=(x000 x0):False
% Found (x000 x0) as proof of False
% Found ((((x00 Xp1) Xp0) Xx0) x0) as proof of False
% Found ((((x00 Xp1) Xp0) Xx0) x0) as proof of False
% Found (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)) as proof of False
% Found (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)) as proof of (((x Xx2) Xx1)->False)
% Found (or_intror00 (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found ((or_intror0 (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (fun (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)))) as proof of ((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))
% Found (fun (Xp1:((Prop->Prop)->Prop)) (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)))) as proof of (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)))
% Found (fun (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)))) as proof of (forall (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))))
% Found (fun (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)))) as proof of (forall (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))))
% Found (fun (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)))) as proof of (forall (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))))
% Found (fun (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)))) as proof of (forall (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))))
% Found (fun (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)) (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_intror ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False)) (fun (x00:((x Xx2) Xx1))=> ((((x00 Xp1) Xp0) Xx0) x0)))) as proof of (forall (Xx0:(Prop->Prop)) (Xx1:(Prop->Prop)) (Xx2:(Prop->Prop)) (Xp0:((Prop->Prop)->Prop)) (Xp1:((Prop->Prop)->Prop)), (((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False))->((or ((or (((x Xx1) Xx0)->False)) (((x Xx2) Xx0)->False))) (((x Xx2) Xx1)->False))))
% Found x03:(Xp1 Xx1)
% Instantiate: x:=(fun (x2:(Prop->Prop)) (x10:(Prop->Prop))=> (Xp1 x2)):((Prop->Prop)->((Prop->Prop)->Prop))
% Found (fun (x03:(Xp1 Xx1))=> x03) as proof of ((x Xx1) Xx0)
% Found (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03) as proof of ((Xp1 Xx1)->((x Xx1) Xx0))
% Found (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03) as proof of (((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->((x Xx1) Xx0)))
% Found (and_rect10 (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found ((and_rect1 ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)) as proof of ((x Xx1) Xx0)
% Found (fun (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of ((x Xx1) Xx0)
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of (((Xp1 Xx2)->False)->((x Xx1) Xx0))
% Found (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))) as proof of (((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->((x Xx1) Xx0)))
% Found (and_rect00 (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found ((and_rect0 ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))) as proof of ((x Xx1) Xx0)
% Found (or_introl00 (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found ((or_introl0 ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))) as proof of ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))
% Found (or_intror00 (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0)))
% Found ((or_intror0 ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0)))
% Found (((or_intror ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0)))
% Found (((or_intror ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))) as proof of ((or ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0)))
% Found (or_comm_i00 (((or_intror ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found ((or_comm_i0 ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_intror ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (((or_comm_i ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_intror ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03))))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found (fun (x0:((and ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)))=> (((or_comm_i ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_intror ((x Xx2) Xx1)) ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) (((or_introl ((x Xx1) Xx0)) ((x Xx2) Xx0)) (((fun (P:Type) (x1:(((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))->(((Xp1 Xx2)->False)->P)))=> (((((and_rect ((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) ((Xp1 Xx2)->False)) P) x1) x0)) ((x Xx1) Xx0)) (fun (x00:((and ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1))) (x01:((Xp1 Xx2)->False))=> (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) ((x Xx1) Xx0)) (fun (x02:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x03:(Xp1 Xx1))=> x03)))))))) as proof of ((or ((or ((x Xx1) Xx0)) ((x Xx2) Xx0))) ((x Xx2) Xx1))
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:(Xp1 Xx1))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x2:(Xp1 Xx1))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of ((Xp1 Xx1)->(Xp1 Xx2))
% Found (fun (x1:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x2:(Xp1 Xx1))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->(Xp1 Xx2)))
% Found (and_rect10 (fun (x1:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x2:(Xp1 Xx1))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect1 (Xp1 Xx2)) (fun (x1:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x2:(Xp1 Xx1))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) (Xp1 Xx2)) (fun (x1:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x2:(Xp1 Xx1))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))->((Xp1 Xx1)->P)))=> (((((and_rect ((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (Xp1 Xx1)) P) x1) x00)) (Xp1 Xx2)) (fun (x1:((and ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False))) (x2:(Xp1 Xx1))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((Xp1 Xx0)->False)->(Xp1 Xx2))
% Found (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->(Xp1 Xx2)))
% Found (and_rect20 (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect2 (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->P)))=> (((((and_rect ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False)) P) x1) x02)) (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->P)))=> (((((and_rect ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False)) P) x1) x02)) (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((Xp1 Xx0)->False)->(Xp1 Xx2))
% Found (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->(Xp1 Xx2)))
% Found (and_rect20 (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect2 (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->P)))=> (((((and_rect ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False)) P) x1) x02)) (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->P)))=> (((((and_rect ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False)) P) x1) x02)) (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((Xp1 Xx0)->False)->(Xp1 Xx2))
% Found (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->(Xp1 Xx2)))
% Found (and_rect20 (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect2 (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->P)))=> (((((and_rect ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False)) P) x1) x02)) (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))->(((Xp1 Xx0)->False)->P)))=> (((((and_rect ((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) ((Xp1 Xx0)->False)) P) x1) x02)) (Xp1 Xx2)) (fun (x1:((and ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False))) (x2:((Xp1 Xx0)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (Xp1 Xx0)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx0))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx0)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found ((and_rect3 (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (Xp1 Xx0)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx0))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx0)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found ((and_rect3 (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0))) as proof of (Xp1 Xx0)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx0))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx0)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found ((and_rect3 (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx2)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found (fun (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (Xp1 Xx0)
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx0))
% Found (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx0)))
% Found (and_rect30 (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found ((and_rect3 (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found (((fun (P:Type) (x1:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x1) x04)) (Xp1 Xx0)) (fun (x1:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x2:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)))) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x3:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x3) x1)) (Xp1 Xx2)) (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x3:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x3) x1)) (Xp1 Xx2)) (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x3:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x3) x1)) (Xp1 Xx2)) (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x3:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x3) x1)) (Xp1 Xx2)) (fun (x3:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x4:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x20)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x051)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x051)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x070)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x011)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found (fun (x6:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2))) as proof of (Xp1 Xx2)
% Found (fun (x5:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x6:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2))) as proof of (((Xp0 Xx2)->False)->(Xp1 Xx2))
% Found (fun (x5:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x6:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2))) as proof of (((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->(Xp1 Xx2)))
% Found (and_rect30 (fun (x5:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x6:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found ((and_rect3 (Xp1 Xx2)) (fun (x5:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x6:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x5:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x5) x3)) (Xp1 Xx2)) (fun (x5:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x6:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found (((fun (P:Type) (x5:(((and (Xp0 Xx0)) ((Xp0 Xx1)->False))->(((Xp0 Xx2)->False)->P)))=> (((((and_rect ((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) ((Xp0 Xx2)->False)) P) x5) x3)) (Xp1 Xx2)) (fun (x5:((and (Xp0 Xx0)) ((Xp0 Xx1)->False))) (x6:((Xp0 Xx2)->False))=> ((fun (P:Type)=> ((False_rect P) x40)) (Xp1 Xx2)))) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp0 Xx2)):(Xp0 Xx2)
% Found (False_rect0 (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp0 Xx2)) as proof of (Xp0 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x051)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x051)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x051)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x051)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x050)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx2)):(Xp1 Xx2)
% Found (False_rect0 (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx2)) as proof of (Xp1 Xx2)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found ((fun (P:Type)=> ((False_rect P) x010)) (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found False_rect00:=(False_rect0 (Xp1 Xx0)):(Xp1 Xx0)
% Found (False_rect0 (Xp1 Xx0)) as proof of (Xp1 Xx0)
% Found (
% EOF
%------------------------------------------------------------------------------