%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV034^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n189.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 13:33:37 EDT 2014

% Result   : Timeout 300.07s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV034^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n189.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 07:38:06 CDT 2014
% % CPUTime  : 300.07 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x16bdab8>, <kernel.Type object at 0x16bdcf8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1b141b8>, <kernel.Type object at 0x16bdb90>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (forall (Xp:(a->(a->Prop))) (Xq:(a->(b->(b->Prop)))) (Xf:(a->b)) (Xg:(a->b)), ((forall (Xx:a), (((Xp Xx) Xx)->(((Xq Xx) (Xf Xx)) (Xg Xx))))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xf Xy))))->(((and ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((and ((and (forall (Xx0:b) (Xy0:b), ((((Xq Xx) Xx0) Xy0)->(((Xq Xx) Xy0) Xx0)))) (forall (Xx0:b) (Xy0:b) (Xz:b), (((and (((Xq Xx) Xx0) Xy0)) (((Xq Xx) Xy0) Xz))->(((Xq Xx) Xx0) Xz))))) (((eq (b->(b->Prop))) (Xq Xx)) (Xq Xy)))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xg Xy))))))))) of role conjecture named cTHM518_pme
% Conjecture to prove = (forall (Xp:(a->(a->Prop))) (Xq:(a->(b->(b->Prop)))) (Xf:(a->b)) (Xg:(a->b)), ((forall (Xx:a), (((Xp Xx) Xx)->(((Xq Xx) (Xf Xx)) (Xg Xx))))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xf Xy))))->(((and ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((and ((and (forall (Xx0:b) (Xy0:b), ((((Xq Xx) Xx0) Xy0)->(((Xq Xx) Xy0) Xx0)))) (forall (Xx0:b) (Xy0:b) (Xz:b), (((and (((Xq Xx) Xx0) Xy0)) (((Xq Xx) Xy0) Xz))->(((Xq Xx) Xx0) Xz))))) (((eq (b->(b->Prop))) (Xq Xx)) (Xq Xy)))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xg Xy))))))))):Prop
% Parameter a_DUMMY:a.
% Parameter b_DUMMY:b.
% We need to prove ['(forall (Xp:(a->(a->Prop))) (Xq:(a->(b->(b->Prop)))) (Xf:(a->b)) (Xg:(a->b)), ((forall (Xx:a), (((Xp Xx) Xx)->(((Xq Xx) (Xf Xx)) (Xg Xx))))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xf Xy))))->(((and ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((and ((and (forall (Xx0:b) (Xy0:b), ((((Xq Xx) Xx0) Xy0)->(((Xq Xx) Xy0) Xx0)))) (forall (Xx0:b) (Xy0:b) (Xz:b), (((and (((Xq Xx) Xx0) Xy0)) (((Xq Xx) Xy0) Xz))->(((Xq Xx) Xx0) Xz))))) (((eq (b->(b->Prop))) (Xq Xx)) (Xq Xy)))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xg Xy)))))))))']
% Parameter a:Type.
% Parameter b:Type.
% Trying to prove (forall (Xp:(a->(a->Prop))) (Xq:(a->(b->(b->Prop)))) (Xf:(a->b)) (Xg:(a->b)), ((forall (Xx:a), (((Xp Xx) Xx)->(((Xq Xx) (Xf Xx)) (Xg Xx))))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xf Xy))))->(((and ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp))->((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((and ((and (forall (Xx0:b) (Xy0:b), ((((Xq Xx) Xx0) Xy0)->(((Xq Xx) Xy0) Xx0)))) (forall (Xx0:b) (Xy0:b) (Xz:b), (((and (((Xq Xx) Xx0) Xy0)) (((Xq Xx) Xy0) Xz))->(((Xq Xx) Xx0) Xz))))) (((eq (b->(b->Prop))) (Xq Xx)) (Xq Xy)))))->(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->(((Xq Xx) (Xf Xx)) (Xg Xy)))))))))
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P b0)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P b0))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P b0)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found ((and_rect1 (P b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P b0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P b0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P b0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P b0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found ((and_rect1 (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P b0)
% Found (fun (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (P b0)
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of ((((eq (a->(a->Prop))) Xp) Xp)->(P b0))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->(P b0)))
% Found (and_rect00 (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P b0)
% Found ((and_rect0 (P b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P b0)
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P b0)
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P b0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found (fun (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P (Xg a0))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P (Xg a0)))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P (Xg a0))))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (Xg a0))
% Found ((and_rect1 (P (Xg a0))) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (Xg a0))
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (Xg a0))
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (Xg a0))
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P (Xg a0))
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P (Xg a0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P (Xg a0)))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P (Xg a0))))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (Xg a0))
% Found ((and_rect1 (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (Xg a0))
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P (Xg a0))
% Found (fun (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (P (Xg a0))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of ((((eq (a->(a->Prop))) Xp) Xp)->(P (Xg a0)))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->(P (Xg a0))))
% Found (and_rect00 (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P (Xg a0))
% Found ((and_rect0 (P (Xg a0))) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P (Xg a0))
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P (Xg a0))) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P (Xg a0))
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P (Xg a0))) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P (Xg a0))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P (Xg a0))
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P a0))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P a0)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect1 (P a0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P a0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P a0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect1 (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (fun (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (P a0)
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of ((((eq (a->(a->Prop))) Xp) Xp)->(P a0))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->(P a0)))
% Found (and_rect00 (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found ((and_rect0 (P a0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P a0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P a0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P a0))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P a0)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect1 (P a0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P0)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P a0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P a0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P a0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P a0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found ((and_rect1 (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P a0)
% Found (fun (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (P a0)
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of ((((eq (a->(a->Prop))) Xp) Xp)->(P a0))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->(P a0)))
% Found (and_rect00 (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found ((and_rect0 (P a0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P a0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found (((fun (P0:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P0)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P0) x4) x1)) (P a0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P0:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P0)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P0) x6) x4)) (P a0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 (Xg a0)):(((eq b) (Xg a0)) (Xg a0))
% Found (eq_ref0 (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found ((eq_ref b) (Xg a0)) as proof of (((eq b) (Xg a0)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 (Xg Xy)):(((eq b) (Xg Xy)) (Xg Xy))
% Found (eq_ref0 (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found ((eq_ref b) (Xg Xy)) as proof of (((eq b) (Xg Xy)) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 (Xg a00))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 (Xg a00)))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 (Xg a00))))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found ((and_rect1 (P0 (Xg a00))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 (Xg a00))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 (Xg a00))) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b00)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b0)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P0 b0))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P0 b0)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found ((and_rect1 (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found ((and_rect1 (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found ((and_rect1 (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (fun (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (P0 b0)
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of ((((eq (a->(a->Prop))) Xp) Xp)->(P0 b0))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->(P0 b0)))
% Found (and_rect00 (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b0)
% Found ((and_rect0 (P0 b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P1)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P1) x4) x1)) (P0 b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P1)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P1) x4) x1)) (P0 b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found ((eq_ref b) b0) as proof of (((eq b) b0) (Xg a0))
% Found eq_ref00:=(eq_ref0 a1):(((eq b) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found ((eq_ref b) a1) as proof of (((eq b) a1) b0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b00)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P0 b00))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P0 b00)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found ((and_rect1 (P0 b00)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b00)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b00))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b00)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found ((and_rect1 (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b00)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b00)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b00))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b00)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found ((and_rect1 (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b00)
% Found (fun (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (P0 b00)
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of ((((eq (a->(a->Prop))) Xp) Xp)->(P0 b00))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->(P0 b00)))
% Found (and_rect00 (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b00)
% Found ((and_rect0 (P0 b00)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b00)
% Found (((fun (P1:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P1)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P1) x4) x1)) (P0 b00)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b00)
% Found (((fun (P1:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P1)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P1) x4) x1)) (P0 b00)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b00)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b00)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 (Xg a00))
% Found (fun (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 (Xg a00))
% Found (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->(P0 (Xg a00)))
% Found (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->(P0 (Xg a00))))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found ((and_rect1 (P0 (Xg a00))) (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 (Xg a00))) (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 (Xg a00))) (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 (Xg a00))
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b0)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P0 b0))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->(P0 b0)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found ((and_rect1 (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found (fun (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b0)
% Found (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->(P0 b0))
% Found (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->(P0 b0)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found ((and_rect1 (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))->P1)))=> (((((and_rect (forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx0:a) (Xy:a), (((Xp Xx0) Xy)->((Xp Xy) Xx0)))) (x7:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xp Xx0) Xy)) ((Xp Xy) Xz))->((Xp Xx0) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found ((and_rect1 (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found x6000:=(x600 x3):((Xp Xy0) Xx)
% Found (x600 x3) as proof of ((Xp Xy0) Xx)
% Found ((x60 Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found (((x6 Xx) Xy0) x3) as proof of ((Xp Xy0) Xx)
% Found ((conj00 x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (((conj0 ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xx))
% Found (x7000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xx)) x3) (((x6 Xx) Xy0) x3))) as proof of ((Xp Xx) Xx)
% Found ((x700 Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> ((x70 Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))) as proof of ((Xp Xx) Xx)
% Found (x8 (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))) as proof of (P0 b0)
% Found (fun (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of (P0 b0)
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0))
% Found (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))) as proof of ((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->(P0 b0)))
% Found (and_rect10 (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found ((and_rect1 (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))) as proof of (P0 b0)
% Found (fun (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (P0 b0)
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of ((((eq (a->(a->Prop))) Xp) Xp)->(P0 b0))
% Found (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3))))))) as proof of (((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->(P0 b0)))
% Found (and_rect00 (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b0)
% Found ((and_rect0 (P0 b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P1)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P1) x4) x1)) (P0 b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and_rect (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))) P1) x6) x4)) (P0 b0)) (fun (x6:(forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (x7:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))=> ((x Xx) (((fun (Xy0:a)=> (((x7 Xx) Xy0) Xx)) Xy) ((((conj ((Xp Xx) Xy)) ((Xp Xy) Xx)) x3) (((x6 Xx) Xy) x3)))))))) as proof of (P0 b0)
% Found (((fun (P1:Type) (x4:(((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))->((((eq (a->(a->Prop))) Xp) Xp)->P1)))=> (((((and_rect ((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (((eq (a->(a->Prop))) Xp) Xp)) P1) x4) x1)) (P0 b0)) (fun (x4:((and (forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz))))) (x5:(((eq (a->(a->Prop))) Xp) Xp))=> (((fun (P1:Type) (x6:((forall (Xx:a) (Xy:a), (((Xp Xx) Xy)->((Xp Xy) Xx)))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xp Xx) Xy)) ((Xp Xy) Xz))->((Xp Xx) Xz)))->P1)))=> (((((and
% EOF
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