%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV118^5 : 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 13:33:45 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV118^5 : 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 08:08:26 CDT 2014
% % CPUTime  : 300.10 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1f91710>, <kernel.Type object at 0x1f90f38>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a), ((iff (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->(Xq Xw)))) (forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(a->(a->Prop))), (((and ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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))))->((Xp Xx) Xy))))) of role conjecture named cTHM526_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a), ((iff (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->(Xq Xw)))) (forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(a->(a->Prop))), (((and ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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))))->((Xp Xx) Xy))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a), ((iff (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->(Xq Xw)))) (forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(a->(a->Prop))), (((and ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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))))->((Xp Xx) Xy)))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a), ((iff (forall (Xq:(a->Prop)), (((and (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->(Xq Xw)))) (forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(a->(a->Prop))), (((and ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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))))->((Xp Xx) Xy)))))
% Found x4:(Xq Xz)
% Found (fun (x4:(Xq Xz))=> x4) as proof of (Xq Xz)
% Found (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4) as proof of ((Xq Xz)->(Xq Xz))
% Found (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4) as proof of ((Xq Xy0)->((Xq Xz)->(Xq Xz)))
% Found (and_rect00 (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4)) as proof of (Xq Xz)
% Found ((and_rect0 (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4)) as proof of (Xq Xz)
% Found (fun (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (Xq Xz)
% Found (fun (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))
% Found (fun (Xy0:a) (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (forall (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x4:(Xq Xz)
% Found (fun (x4:(Xq Xz))=> x4) as proof of (Xq Xz)
% Found (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4) as proof of ((Xq Xz)->(Xq Xz))
% Found (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4) as proof of ((Xq Xy0)->((Xq Xz)->(Xq Xz)))
% Found (and_rect00 (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4)) as proof of (Xq Xz)
% Found ((and_rect0 (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4)) as proof of (Xq Xz)
% Found (fun (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (Xq Xz)
% Found (fun (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))
% Found (fun (Xy0:a) (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (forall (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x2:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x3:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x3) x2)) (Xq Xz)) (fun (x3:(Xq Xy0)) (x4:(Xq Xz))=> x4))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x6:(Xq Xz)
% Found (fun (x6:(Xq Xz))=> x6) as proof of (Xq Xz)
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xz)->(Xq Xz))
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xy0)->((Xq Xz)->(Xq Xz)))
% Found (and_rect10 (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (fun (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (Xq Xz)
% Found (fun (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))
% Found (fun (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x6:(Xq Xz)
% Found (fun (x6:(Xq Xz))=> x6) as proof of (Xq Xz)
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xz)->(Xq Xz))
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xy0)->((Xq Xz)->(Xq Xz)))
% Found (and_rect10 (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (fun (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (Xq Xz)
% Found (fun (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))
% Found (fun (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found or_introl00:=(or_introl0 ((Xr Xy0) Xx0)):(((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (or_introl0 ((Xr Xy0) Xx0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found or_comm_i00:=(or_comm_i0 ((Xr Xy0) Xx0)):(((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (or_comm_i0 ((Xr Xy0) Xx0)) as proof of (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)) as proof of (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found ((conj20 (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found (((conj2 (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found x50:=(x5 x20):(Xq Xz)
% Found (x5 x20) as proof of (Xq Xz)
% Found (fun (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (Xq Xz)
% Found (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->(Xq Xz))
% Found (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->(Xq Xz)))
% Found (and_rect10 (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (fun (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (Xq Xz)
% Found (fun (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))
% Found (fun (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))
% Found (fun (Xy0:a) (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xz:a), (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xy0:a) (Xz:a), (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x6:(Xq Xz)
% Found (fun (x6:(Xq Xz))=> x6) as proof of (Xq Xz)
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xz)->(Xq Xz))
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xy0)->((Xq Xz)->(Xq Xz)))
% Found (and_rect10 (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (fun (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (Xq Xz)
% Found (fun (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))
% Found (fun (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x3000:=(x300 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x300 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x30 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x30 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x6:(Xq Xz)
% Found (fun (x6:(Xq Xz))=> x6) as proof of (Xq Xz)
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xz)->(Xq Xz))
% Found (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6) as proof of ((Xq Xy0)->((Xq Xz)->(Xq Xz)))
% Found (and_rect10 (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6)) as proof of (Xq Xz)
% Found (fun (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (Xq Xz)
% Found (fun (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))
% Found (fun (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and (Xq Xy0)) (Xq Xz)))=> (((fun (P:Type) (x5:((Xq Xy0)->((Xq Xz)->P)))=> (((((and_rect (Xq Xy0)) (Xq Xz)) P) x5) x4)) (Xq Xz)) (fun (x5:(Xq Xy0)) (x6:(Xq Xz))=> x6))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found or_comm_i00:=(or_comm_i0 ((Xr Xy0) Xx0)):(((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (or_comm_i0 ((Xr Xy0) Xx0)) as proof of (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)) as proof of (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found or_introl00:=(or_introl0 ((Xr Xy0) Xx0)):(((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (or_introl0 ((Xr Xy0) Xx0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found ((conj20 (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found (((conj2 (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (fun (Xx0:a) (Xy0:a)=> ((or_introl ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))))
% Found x50:=(x5 x20):(Xq Xz)
% Found (x5 x20) as proof of (Xq Xz)
% Found (fun (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (Xq Xz)
% Found (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->(Xq Xz))
% Found (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->(Xq Xz)))
% Found (and_rect10 (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (fun (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (Xq Xz)
% Found (fun (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))
% Found (fun (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))
% Found (fun (Xy0:a) (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xz:a), (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xy0:a) (Xz:a), (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x3:((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))->(Xq Xz)))))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found or_intror00:=(or_intror0 ((Xr Xx0) Xy0)):(((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (or_intror0 ((Xr Xx0) Xy0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found or_comm_i10:=(or_comm_i1 ((Xr Xx0) Xy0)):(((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (or_comm_i1 ((Xr Xx0) Xy0)) as proof of (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)) as proof of (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found ((conj20 (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found (((conj2 (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6) as proof of (((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))
% Found (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6) as proof of (((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))
% Found (and_rect10 (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6)) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found ((and_rect1 ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6)) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6)) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))
% Found (fun (Xy0:a) (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (forall (Xz:a), (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (forall (Xy0:a) (Xz:a), (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x500:=(x50 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x50 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x3000:=(x300 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x300 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x30 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x30 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x500:=(x50 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x50 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found or_comm_i10:=(or_comm_i1 ((Xr Xx0) Xy0)):(((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (or_comm_i1 ((Xr Xx0) Xy0)) as proof of (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)) as proof of (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))
% Found or_intror00:=(or_intror0 ((Xr Xx0) Xy0)):(((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (or_intror0 ((Xr Xx0) Xy0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))
% Found ((conj20 (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found (((conj2 (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found ((((conj (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0))))) (fun (Xx0:a) (Xy0:a)=> ((or_intror ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) (fun (Xx0:a) (Xy0:a)=> ((or_comm_i ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0)))) as proof of ((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))))) (forall (Xx0:a) (Xy0:a), (((or ((Xr Xy0) Xx0)) ((Xr Xx0) Xy0))->((or ((Xr Xx0) Xy0)) ((Xr Xy0) Xx0)))))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6) as proof of (((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))
% Found (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6) as proof of (((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))
% Found (and_rect10 (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6)) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found ((and_rect1 ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6)) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6)) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))
% Found (fun (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))
% Found (fun (Xy0:a) (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (forall (Xz:a), (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (forall (Xy0:a) (Xz:a), (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz:a) (x4:((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))->(((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))->P)))=> (((((and_rect ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) P) x5) x4)) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv)))) (fun (x5:((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) (x6:((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))=> x6))) as proof of (a->(forall (Xy0:a) (Xz:a), (((and ((and (Xq Xv)) ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv)))) ((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))->((and (Xq Xv)) ((or ((Xr Xv) Xz)) ((Xr Xz) Xv))))))
% Found x3000:=(x300 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x300 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x30 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x30 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x300:=(x30 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x30 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x3 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x500:=(x50 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x50 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x500:=(x50 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x50 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x6:((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of ((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x500:=(x50 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x50 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x6:((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of ((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x4:(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found x4 as proof of (Xq Xv)
% Found x5:((Xr Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> x5) as proof of ((Xr Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> x5) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x4:(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found x4 as proof of (Xq Xv)
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x4:(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found x4 as proof of (Xq Xv)
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x7:((Xr Xw) Xx)
% Found (fun (x7:((Xr Xw) Xx))=> x7) as proof of ((Xr Xw) Xx)
% Found (fun (x7:((Xr Xw) Xx))=> x7) as proof of (((Xr Xw) Xx)->((Xr Xw) Xx))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x3000:=(x300 x7):((Xp Xw) Xx)
% Found (x300 x7) as proof of ((Xp Xw) Xx)
% Found ((x30 Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (x400 (((x3 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found ((x40 Xx) (((x3 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (((x4 Xw) Xx) (((x3 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x30:=(x3 x20):(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found (x3 x20) as proof of (Xq Xv)
% Found (x3 x20) as proof of (Xq Xv)
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x4000:=(x400 x7):((Xp Xw) Xx)
% Found (x400 x7) as proof of ((Xp Xw) Xx)
% Found ((x40 Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (x500 (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found ((x50 Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (((x5 Xw) Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x4000:=(x400 x7):((Xp Xw) Xx)
% Found (x400 x7) as proof of ((Xp Xw) Xx)
% Found ((x40 Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (x500 (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found ((x50 Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (((x5 Xw) Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x3000:=(x300 x6):((Xp Xw) Xx)
% Found (x300 x6) as proof of ((Xp Xw) Xx)
% Found ((x30 Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (x4000 (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found ((x400 Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (((x40 Xw) Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (fun (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))))
% Found x500:=(x50 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x50 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x500:=(x50 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x50 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x400:=(x40 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x40 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x4 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x3000:=(x300 x6):((Xp Xw) Xx)
% Found (x300 x6) as proof of ((Xp Xw) Xx)
% Found ((x30 Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (x400 (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found ((x40 Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (((x4 Xw) Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))))
% Found x3000:=(x300 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x300 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x30 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x30 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x500:=(x50 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x50 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found ((x5 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x30000:=(x3000 x5):((Xp Xw) Xx)
% Found (x3000 x5) as proof of ((Xp Xw) Xx)
% Found ((x300 Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x30 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x30 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (x4000 (((x30 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found ((x400 Xx) (((x30 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (((x40 Xw) Xx) (((x30 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (fun (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of ((Xp Xx) Xw)
% Found (fun (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))))
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))))
% Found x6:((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of ((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x4:(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found x4 as proof of (Xq Xv)
% Found x5:((Xr Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> x5) as proof of ((Xr Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> x5) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x6:((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of ((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x7:((Xr Xw) Xx)
% Found (fun (x7:((Xr Xw) Xx))=> x7) as proof of ((Xr Xw) Xx)
% Found (fun (x7:((Xr Xw) Xx))=> x7) as proof of (((Xr Xw) Xx)->((Xr Xw) Xx))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x5:((Xr Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> x5) as proof of ((Xr Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> x5) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x4:(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found x4 as proof of (Xq Xv)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x6:((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of ((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x2:(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found x2 as proof of (Xq Xv)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x4:(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found x4 as proof of (Xq Xv)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy0:a) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x7:((Xr Xw) Xx)
% Found (fun (x7:((Xr Xw) Xx))=> x7) as proof of ((Xr Xw) Xx)
% Found (fun (x7:((Xr Xw) Xx))=> x7) as proof of (((Xr Xw) Xx)->((Xr Xw) Xx))
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x4000:=(x400 x3):((Xp Xx) Xw)
% Found (x400 x3) as proof of ((Xp Xx) Xw)
% Found ((x40 Xw) x3) as proof of ((Xp Xx) Xw)
% Found (((x4 Xx) Xw) x3) as proof of ((Xp Xx) Xw)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3)) as proof of ((Xp Xx) Xw)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))) as proof of ((Xp Xx) Xw)
% Found (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3)))) as proof of ((Xp Xx) Xw)
% Found (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3)))) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x6000:=(x600 x5):((Xp Xx) Xw)
% Found (x600 x5) as proof of ((Xp Xx) Xw)
% Found ((x60 Xw) x5) as proof of ((Xp Xx) Xw)
% Found (((x6 Xx) Xw) x5) as proof of ((Xp Xx) Xw)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)) as proof of ((Xp Xx) Xw)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)))) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x6000:=(x600 x5):((Xp Xx) Xw)
% Found (x600 x5) as proof of ((Xp Xx) Xw)
% Found ((x60 Xw) x5) as proof of ((Xp Xx) Xw)
% Found (((x6 Xx) Xw) x5) as proof of ((Xp Xx) Xw)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)) as proof of ((Xp Xx) Xw)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5)))) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x60:=(x6 x40):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x6 x40) as proof of ((Xp Xx) Xy0)
% Found (x6 x40) as proof of ((Xp Xx) Xy0)
% Found x20:(forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))
% Found x20 as proof of (forall (Xv:a) (Xw:a), (((and (Xq Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))->(Xq Xw)))
% Found x60:=(x6 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x6 x20) as proof of ((Xp Xx) Xy0)
% Found (x6 x20) as proof of ((Xp Xx) Xy0)
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x3000:=(x300 x7):((Xp Xw) Xx)
% Found (x300 x7) as proof of ((Xp Xw) Xx)
% Found ((x30 Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (x400 (((x3 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found ((x40 Xx) (((x3 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (((x4 Xw) Xx) (((x3 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x7))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x30:=(x3 x20):(Xq Xy0)
% Instantiate: Xv:=Xy0:a
% Found (x3 x20) as proof of (Xq Xv)
% Found (x3 x20) as proof of (Xq Xv)
% Found x5000:=(x500 x4):((Xp Xx) Xw)
% Found (x500 x4) as proof of ((Xp Xx) Xw)
% Found ((x50 Xw) x4) as proof of ((Xp Xx) Xw)
% Found (((x5 Xx) Xw) x4) as proof of ((Xp Xx) Xw)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4)) as proof of ((Xp Xx) Xw)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4)) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4)))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4)))) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found x500:=(x50 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x50 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x4:(Xq Xv)
% Found (fun (x4:(Xq Xv))=> x4) as proof of (Xq Xv)
% Found (fun (Xy0:a) (x4:(Xq Xv))=> x4) as proof of ((Xq Xv)->(Xq Xv))
% Found (fun (Xx0:a) (Xy0:a) (x4:(Xq Xv))=> x4) as proof of (a->((Xq Xv)->(Xq Xv)))
% Found (fun (Xx0:a) (Xy0:a) (x4:(Xq Xv))=> x4) as proof of (a->(a->((Xq Xv)->(Xq Xv))))
% Found x4000:=(x400 x7):((Xp Xw) Xx)
% Found (x400 x7) as proof of ((Xp Xw) Xx)
% Found ((x40 Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (x500 (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found ((x50 Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (((x5 Xw) Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x6:((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of ((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x300:=(x30 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x30 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x3 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x4000:=(x400 x7):((Xp Xw) Xx)
% Found (x400 x7) as proof of ((Xp Xw) Xx)
% Found ((x40 Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x7) as proof of ((Xp Xw) Xx)
% Found (x500 (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found ((x50 Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (((x5 Xw) Xx) (((x4 Xw) Xx) x7)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of ((Xp Xx) Xw)
% Found (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7)))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x6:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x7:(((Xr Xx) Xw)->P)) (x8:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x7) x8) x6)) ((Xp Xx) Xw)) ((x4 Xx) Xw)) (fun (x7:((Xr Xw) Xx))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x7))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x60:=(x6 x40):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x6 x40) as proof of ((Xp Xx) Xy0)
% Found (x6 x40) as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x4000:=(x400 x3):((Xp Xw) Xx)
% Found (x400 x3) as proof of ((Xp Xw) Xx)
% Found ((x40 Xx) x3) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x3) as proof of ((Xp Xw) Xx)
% Found (((x4 Xw) Xx) x3) as proof of ((Xp Xw) Xx)
% Found (x500 (((x4 Xw) Xx) x3)) as proof of ((Xp Xx) Xw)
% Found ((x50 Xx) (((x4 Xw) Xx) x3)) as proof of ((Xp Xx) Xw)
% Found (((x5 Xw) Xx) (((x4 Xw) Xx) x3)) as proof of ((Xp Xx) Xw)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3)))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3)))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3)))) as proof of ((Xp Xx) Xw)
% Found (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))))) as proof of ((Xp Xx) Xw)
% Found (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3)))))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3)))))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x3:(((Xr Xx) Xw)->P)) (x4:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x3) x4) x2)) ((Xp Xx) Xw)) (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3)))))) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x3:(((Xr Xx) Xw)->P)) (x4:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x3) x4) x2)) ((Xp Xx) Xw)) (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))))))) as proof of ((Xp Xx) Xw)
% Found (fun (x10:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x3:(((Xr Xx) Xw)->P)) (x4:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x3) x4) x2)) ((Xp Xx) Xw)) (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x2:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x10:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x3:(((Xr Xx) Xw)->P)) (x4:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x3) x4) x2)) ((Xp Xx) Xw)) (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))))))) as proof of (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x2:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x10:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x3:(((Xr Xx) Xw)->P)) (x4:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x3) x4) x2)) ((Xp Xx) Xw)) (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->(((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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)))->((Xp Xx) Xw))))
% Found (fun (Xw:a) (x2:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x10:((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x3:(((Xr Xx) Xw)->P)) (x4:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x3) x4) x2)) ((Xp Xx) Xw)) (fun (x3:((Xr Xx) Xw))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x4 Xx) Xw) x3))))) (fun (x3:((Xr Xw) Xx))=> (((fun (P:Type) (x4:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x4) x10)) ((Xp Xx) Xw)) (fun (x4:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x5:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xw) Xx) (((x4 Xw) Xx) x3))))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->(((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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)))->((Xp Xx) Xw)))))
% Found x300:=(x30 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x30 x20) as proof of ((Xp Xx) Xy0)
% Found ((x3 x10) x20) as proof of ((Xp Xx) Xy0)
% Found ((x3 x10) x20) as proof of ((Xp Xx) Xy0)
% Found x300:=(x30 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x30 x20) as proof of ((Xp Xx) Xy0)
% Found ((x3 x10) x20) as proof of ((Xp Xx) Xy0)
% Found ((x3 x10) x20) as proof of ((Xp Xx) Xy0)
% Found x300:=(x30 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x30 x20) as proof of ((Xp Xx) Xy0)
% Found ((x3 x10) x20) as proof of ((Xp Xx) Xy0)
% Found (fun (x4:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> ((x3 x10) x20)) as proof of ((Xp Xx) Xy0)
% Found (fun (x3:(((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xp Xx0) Xy00)->((Xp Xy00) Xx0))))->((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv)))) (x4:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> ((x3 x10) x20)) as proof of (((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0))
% Found (fun (x3:(((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xp Xx0) Xy00)->((Xp Xy00) Xx0))))->((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv)))) (x4:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> ((x3 x10) x20)) as proof of ((((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xp Xx0) Xy00)->((Xp Xy00) Xx0))))->((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv)))->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0)))
% Found (and_rect10 (fun (x3:(((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xp Xx0) Xy00)->((Xp Xy00) Xx0))))->((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv)))) (x4:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> ((x3 x10) x20))) as proof of ((Xp Xx) Xy0)
% Found ((and_rect1 ((Xp Xx) Xy0)) (fun (x3:(((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xp Xx0) Xy00)->((Xp Xy00) Xx0))))->((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv)))) (x4:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> ((x3 x10) x20))) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x3:((((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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)))->((Xp Xx) Xv)))->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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)))->((Xp Xx) Xv)))) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv))) P) x3) x2)) ((Xp Xx) Xy0)) (fun (x3:(((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xp Xx0) Xy00)->((Xp Xy00) Xx0))))->((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv)))) (x4:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> ((x3 x10) x20))) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x3:((((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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)))->((Xp Xx) Xv)))->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (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)))->((Xp Xx) Xv)))) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv))) P) x3) x2)) ((Xp Xx) Xy0)) (fun (x3:(((and (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xp Xx0) Xy00)->((Xp Xy00) Xx0))))->((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv)))) (x4:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> ((x3 x10) x20))) as proof of ((Xp Xx) Xy0)
% Found x500:=(x50 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x50 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x500:=(x50 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x50 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x5 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x3000:=(x300 x6):((Xp Xw) Xx)
% Found (x300 x6) as proof of ((Xp Xw) Xx)
% Found ((x30 Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (x4000 (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found ((x400 Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (((x40 Xw) Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (fun (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))))
% Found x6000:=(x600 x5):((Xp Xw) Xx)
% Found (x600 x5) as proof of ((Xp Xw) Xx)
% Found ((x60 Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x6 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x6 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (x700 (((x6 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found ((x70 Xx) (((x6 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (((x7 Xw) Xx) (((x6 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x2)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (fun (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5) as proof of ((Xp Xx) Xy0)
% Found (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5) as proof of (((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0))
% Found (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5) as proof of (((Xp Xx) Xv)->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0)))
% Found (and_rect10 (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found ((and_rect1 ((Xp Xx) Xy0)) (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect ((Xp Xx) Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv))) P) x5) x4)) ((Xp Xx) Xy0)) (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect ((Xp Xx) Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv))) P) x5) x4)) ((Xp Xx) Xy0)) (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x60:=(x6 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x6 x20) as proof of ((Xp Xx) Xy0)
% Found (x6 x20) as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x6000:=(x600 x5):((Xp Xw) Xx)
% Found (x600 x5) as proof of ((Xp Xw) Xx)
% Found ((x60 Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x6 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x6 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (x700 (((x6 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found ((x70 Xx) (((x6 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (((x7 Xw) Xx) (((x6 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5)))))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx)))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) (fun (x5:((Xr Xx) Xw))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xx) Xw) x5))))) (fun (x5:((Xr Xw) Xx))=> (((fun (P:Type) (x6:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x6) x1)) ((Xp Xx) Xw)) (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x7:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x7 Xw) Xx) (((x6 Xw) Xx) x5))))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((Xp Xx) Xw)))
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (fun (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5) as proof of ((Xp Xx) Xy0)
% Found (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5) as proof of (((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0))
% Found (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5) as proof of (((Xp Xx) Xv)->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0)))
% Found (and_rect10 (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found ((and_rect1 ((Xp Xx) Xy0)) (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect ((Xp Xx) Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv))) P) x5) x4)) ((Xp Xx) Xy0)) (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect ((Xp Xx) Xv)) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv))) P) x5) x4)) ((Xp Xx) Xy0)) (fun (x5:((Xp Xx) Xv)) (x6:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> x5)) as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x7:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x7 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x3000:=(x300 x6):((Xp Xw) Xx)
% Found (x300 x6) as proof of ((Xp Xw) Xx)
% Found ((x30 Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (((x3 Xw) Xx) x6) as proof of ((Xp Xw) Xx)
% Found (x400 (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found ((x40 Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (((x4 Xw) Xx) (((x3 Xw) Xx) x6)) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6)))) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x5:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x6:(((Xr Xx) Xw)->P)) (x7:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x6) x7) x5)) ((Xp Xx) Xw)) ((x3 Xx) Xw)) (fun (x6:((Xr Xw) Xx))=> (((x4 Xw) Xx) (((x3 Xw) Xx) x6))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))))
% Found x6:((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of ((Xr Xx) Xw)
% Found (fun (x6:((Xr Xx) Xw))=> x6) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:a
% Found x4 as proof of ((Xr Xv) Xy0)
% Found (or_introl00 x4) as proof of ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv))
% Found ((or_introl0 ((Xr Xy0) Xv)) x4) as proof of ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv))
% Found (((or_introl ((Xr Xv) Xy0)) ((Xr Xy0) Xv)) x4) as proof of ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv))
% Found (((or_introl ((Xr Xv) Xy0)) ((Xr Xy0) Xv)) x4) as proof of ((or ((Xr Xv) Xy0)) ((Xr Xy0) Xv))
% Found x7:((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of ((Xr Xx) Xw)
% Found (fun (x7:((Xr Xx) Xw))=> x7) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found x400:=(x40 Xx):(((Xr Xw) Xx)->((Xp Xw) Xx))
% Found (x40 Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found ((x4 Xw) Xx) as proof of (((Xr Xw) Xx)->((Xp Xw) Xx))
% Found x30000:=(x3000 x5):((Xp Xw) Xx)
% Found (x3000 x5) as proof of ((Xp Xw) Xx)
% Found ((x300 Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x30 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (((x30 Xw) Xx) x5) as proof of ((Xp Xw) Xx)
% Found (x4000 (((x30 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found ((x400 Xx) (((x30 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (((x40 Xw) Xx) (((x30 Xw) Xx) x5)) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5)))) as proof of ((Xp Xx) Xw)
% Found (fun (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of ((Xp Xx) Xw)
% Found (fun (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))))
% Found (fun (Xw:a) (x4:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x30:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x40:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> ((((fun (P:Prop) (x5:(((Xr Xx) Xw)->P)) (x6:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x5) x6) x4)) ((Xp Xx) Xw)) ((x30 Xx) Xw)) (fun (x5:((Xr Xw) Xx))=> (((x40 Xw) Xx) (((x30 Xw) Xx) x5))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))))
% Found x5000:=(x500 x4):((Xp Xw) Xx)
% Found (x500 x4) as proof of ((Xp Xw) Xx)
% Found ((x50 Xx) x4) as proof of ((Xp Xw) Xx)
% Found (((x5 Xw) Xx) x4) as proof of ((Xp Xw) Xx)
% Found (((x5 Xw) Xx) x4) as proof of ((Xp Xw) Xx)
% Found (x600 (((x5 Xw) Xx) x4)) as proof of ((Xp Xx) Xw)
% Found ((x60 Xx) (((x5 Xw) Xx) x4)) as proof of ((Xp Xx) Xw)
% Found (((x6 Xw) Xx) (((x5 Xw) Xx) x4)) as proof of ((Xp Xx) Xw)
% Found (fun (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw))
% Found (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))) as proof of ((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4)))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4)))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4)))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))))) as proof of (((Xr Xw) Xx)->((Xp Xx) Xw))
% Found ((or_ind00 (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))))) (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4)))))) as proof of ((Xp Xx) Xw)
% Found (((or_ind0 ((Xp Xx) Xw)) (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))))) (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4)))))) as proof of ((Xp Xx) Xw)
% Found ((((fun (P:Prop) (x4:(((Xr Xx) Xw)->P)) (x5:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x4) x5) x3)) ((Xp Xx) Xw)) (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))))) (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4)))))) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x4:(((Xr Xx) Xw)->P)) (x5:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x4) x5) x3)) ((Xp Xx) Xw)) (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))))) (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))))))) as proof of ((Xp Xx) Xw)
% Found (fun (x3:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x4:(((Xr Xx) Xw)->P)) (x5:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x4) x5) x3)) ((Xp Xx) Xw)) (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))))) (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))))))) as proof of ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (Xw:a) (x3:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x4:(((Xr Xx) Xw)->P)) (x5:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x4) x5) x3)) ((Xp Xx) Xw)) (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))))) (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))))))) as proof of (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (fun (Xw:a) (x3:((or ((Xr Xx) Xw)) ((Xr Xw) Xx))) (x20:(forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((((fun (P:Prop) (x4:(((Xr Xx) Xw)->P)) (x5:(((Xr Xw) Xx)->P))=> ((((((or_ind ((Xr Xx) Xw)) ((Xr Xw) Xx)) P) x4) x5) x3)) ((Xp Xx) Xw)) (fun (x4:((Xr Xx) Xw))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x5 Xx) Xw) x4))))) (fun (x4:((Xr Xw) Xx))=> (((fun (P:Type) (x5:((forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0)))) P) x5) x1)) ((Xp Xx) Xw)) (fun (x5:(forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x6:(forall (Xx0:a) (Xy0:a), (((Xp Xx0) Xy0)->((Xp Xy0) Xx0))))=> (((x6 Xw) Xx) (((x5 Xw) Xx) x4))))))) as proof of (forall (Xw:a), (((or ((Xr Xx) Xw)) ((Xr Xw) Xx))->((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))))
% Found x40:=(x4 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found x40:=(x4 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found x40:=(x4 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:a
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found (fun (x5:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> (x4 x20)) as proof of ((Xp Xx) Xy0)
% Found (fun (x4:((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))) (x5:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> (x4 x20)) as proof of (((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0))
% Found (fun (x4:((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))) (x5:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> (x4 x20)) as proof of (((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->((Xp Xx) Xy0)))
% Found (and_rect10 (fun (x4:((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))) (x5:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> (x4 x20))) as proof of ((Xp Xx) Xy0)
% Found ((and_rect1 ((Xp Xx) Xy0)) (fun (x4:((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))) (x5:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> (x4 x20))) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))) ((or ((Xr Xv) Xw)) ((Xr Xw) Xv))) P) x4) x3)) ((Xp Xx) Xy0)) (fun (x4:((forall (Xx0:a) (Xy00:a) (Xz:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))) (x5:((or ((Xr Xv) Xw)) ((Xr Xw) Xv)))=> (x4 x20))) as proof of ((Xp Xx) Xy0)
% Found (((fun (P:Type) (x4:(((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xv))->(((or ((Xr Xv) Xw)) ((Xr Xw) Xv))->P)))=> (((((and_rect ((forall (Xx0:a) (Xy0:a) (Xz:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) X
% EOF
%------------------------------------------------------------------------------