TSTP Solution File: SEV060^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV060^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n089.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:40 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  : SEV060^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:50:11 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 (<kernel.Constant object at 0xc0c2d8>, <kernel.Type object at 0xc0c560>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x917e60>, <kernel.Type object at 0xc0c0e0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), (((and (forall (Xx_0:b) (Xy_9:a), (((Xk Xx_0) Xy_9)->((or ((Xs Xx_0) Xy_9)) ((and (((eq b) Xx_0) Xx)) (((eq a) Xy_9) Xy)))))) (((Xk Xx) Xy)->False))->(forall (Xx0:b) (Xy0:a), (((Xk Xx0) Xy0)->((Xs Xx0) Xy0))))) of role conjecture named cTHM173_pme
% Conjecture to prove = (forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), (((and (forall (Xx_0:b) (Xy_9:a), (((Xk Xx_0) Xy_9)->((or ((Xs Xx_0) Xy_9)) ((and (((eq b) Xx_0) Xx)) (((eq a) Xy_9) Xy)))))) (((Xk Xx) Xy)->False))->(forall (Xx0:b) (Xy0:a), (((Xk Xx0) Xy0)->((Xs Xx0) Xy0))))):Prop
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), (((and (forall (Xx_0:b) (Xy_9:a), (((Xk Xx_0) Xy_9)->((or ((Xs Xx_0) Xy_9)) ((and (((eq b) Xx_0) Xx)) (((eq a) Xy_9) Xy)))))) (((Xk Xx) Xy)->False))->(forall (Xx0:b) (Xy0:a), (((Xk Xx0) Xy0)->((Xs Xx0) Xy0)))))']
% Parameter b:Type.
% Parameter a:Type.
% Trying to prove (forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), (((and (forall (Xx_0:b) (Xy_9:a), (((Xk Xx_0) Xy_9)->((or ((Xs Xx_0) Xy_9)) ((and (((eq b) Xx_0) Xx)) (((eq a) Xy_9) Xy)))))) (((Xk Xx) Xy)->False))->(forall (Xx0:b) (Xy0:a), (((Xk Xx0) Xy0)->((Xs Xx0) Xy0)))))
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b0)
% Found False_rect00:=(False_rect0 (P b0)):(P b0)
% Found (False_rect0 (P b0)) as proof of (P b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0)) as proof of (P b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0)) as proof of (P b0)
% Found ((eq_sym0000 ((eq_ref a) Xy0)) ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0))) as proof of ((Xs Xx0) Xy0)
% Found ((eq_sym0000 ((eq_ref a) Xy0)) ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0))) as proof of ((Xs Xx0) Xy0)
% Found (((fun (x3:(((eq a) Xy0) b0))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) Xy0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) Xy0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> ((((eq_sym0 Xy0) Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) Xy0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((((eq_sym a) Xy0) Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) Xy0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((((eq_sym a) Xy0) Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) Xy0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b0)):((Xs Xx0) b0)
% Found (False_rect0 ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of (P b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b0)):((Xs Xx0) b0)
% Found (False_rect0 ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of (P b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b0)):((Xs Xx0) b0)
% Found (False_rect0 ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of (P b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b0)):((Xs Xx0) b0)
% Found (False_rect0 ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of ((Xs Xx0) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) b0)) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of (P a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of (P a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx0) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0010 ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0010 ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) b1))=> ((eq_sym001 x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0010 ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0010 ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) b1))=> ((eq_sym001 x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0010 ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0010 ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) b1))=> ((eq_sym001 x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) Xy0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) Xy0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x23)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x23)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x23)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x23)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x23)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> ((((eq_sym0 a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((((eq_sym a) a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((((eq_sym a) a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 a0)):(P0 a0)
% Found (False_rect0 (P0 a0)) as proof of (P0 a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0)) as proof of (P0 a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0)) as proof of (P0 a0)
% Found (((eq_trans00000 ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0))) as proof of ((Xs Xx0) b0)
% Found (((eq_trans00000 ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) a0) b1)) (x4:(((eq a) b1) b0))=> (((eq_trans0000 x3) x4) (Xs Xx0))) ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) a0) b0)) (x4:(((eq a) b0) b0))=> ((((eq_trans000 b0) x3) x4) (Xs Xx0))) ((eq_ref a) a0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> (((((eq_trans00 b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> (((eq_trans0 a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> ((((eq_trans a) a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> ((((eq_trans a) a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0100 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym010 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym01 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x21)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found ((eq_sym0100 ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) b0)
% Found (((fun (x3:(((eq a) b0) b1))=> ((eq_sym010 x3) (Xs Xx0))) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 (P0 a0)):(P0 a0)
% Found (False_rect0 (P0 a0)) as proof of (P0 a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0)) as proof of (P0 a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0)) as proof of (P0 a0)
% Found (((eq_trans00000 ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0))) as proof of ((Xs Xx0) b0)
% Found (((eq_trans00000 ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) a0) b1)) (x4:(((eq a) b1) b0))=> (((eq_trans0000 x3) x4) (Xs Xx0))) ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) a0) b0)) (x4:(((eq a) b0) b0))=> ((((eq_trans000 b0) x3) x4) (Xs Xx0))) ((eq_ref a) a0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> (((((eq_trans00 b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> (((eq_trans0 a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> ((((eq_trans a) a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> ((((eq_trans a) a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> ((((eq_sym0 a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((((eq_sym a) a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((((eq_sym a) a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 (P0 a0)):(P0 a0)
% Found (False_rect0 (P0 a0)) as proof of (P0 a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0)) as proof of (P0 a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0)) as proof of (P0 a0)
% Found (((eq_trans00000 ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0))) as proof of ((Xs Xx0) b0)
% Found (((eq_trans00000 ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) a0) b1)) (x4:(((eq a) b1) b0))=> (((eq_trans0000 x3) x4) (Xs Xx0))) ((eq_ref a) a0)) ((eq_ref a) b1)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) a0) b0)) (x4:(((eq a) b0) b0))=> ((((eq_trans000 b0) x3) x4) (Xs Xx0))) ((eq_ref a) a0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> (((((eq_trans00 b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> (((eq_trans0 a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> ((((eq_trans a) a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found ((((fun (x3:(((eq a) b0) b0)) (x4:(((eq a) b0) b0))=> ((((((fun (a0:a) (b1:a)=> ((((eq_trans a) a0) b1) b0)) b0) b0) x3) x4) (Xs Xx0))) ((eq_ref a) b0)) ((eq_ref a) b0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b0))) as proof of ((Xs Xx0) b0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((eq_sym00 Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> ((((eq_sym0 a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((((eq_sym a) a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) Xy0))=> (((((eq_sym a) a0) Xy0) x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) Xy0))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b2)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b2)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b2)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 Xy0):(((eq a) Xy0) Xy0)
% Found (eq_ref0 Xy0) as proof of (((eq a) Xy0) b2)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b2)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b2)
% Found ((eq_ref a) Xy0) as proof of (((eq a) Xy0) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym000 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym00 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym000 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym00 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym000 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym00 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym000 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym00 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym000 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym00 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found ((eq_sym0000 ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) b1))=> ((eq_sym000 x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) b1))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((eq_sym00 Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> ((((eq_sym0 Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found (((fun (x3:(((eq a) Xy) Xy))=> (((((eq_sym a) Xy) Xy) x3) (Xk Xx))) ((eq_ref a) Xy)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xk Xx) Xy))) as proof of ((Xk Xx) Xy)
% Found False_rect00:=(False_rect0 (P0 b1)):(P0 b1)
% Found (False_rect0 (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1)) as proof of (P0 b1)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found ((eq_sym0000 ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) (P0 b1))) as proof of ((Xs Xx0) a0)
% Found (((fun (x3:(((eq a) a0) b1))=> ((eq_sym000 x3) (Xs Xx0))) ((eq_ref a) a0)) ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1))) as proof of ((Xs Xx0) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) b1)):((Xs Xx0) b1)
% Found (False_rect0 ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of ((Xs Xx0) b1)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) b1)) as proof of (P0 b1)
% Found False_rect00:=(False_rect0 ((Xs Xx0) a0)):((Xs Xx0) a0)
% Found (False_rect0 ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of ((Xs Xx0) a0)
% Found ((fun (P1:Type)=> ((False_rect P1) x20)) ((Xs Xx0) a0)) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq 
% EOF
%------------------------------------------------------------------------------