TSTP Solution File: SEV075^5 by cocATP---0.2.0

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV075^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n089.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:42 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV075^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:56:06 CDT 2014
% % CPUTime  : 300.09 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))))) of role conjecture named cTHM152_pme
% Conjecture to prove = (forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy)))))']
% Parameter fofType:Type.
% Trying to prove (forall (Xr:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), ((iff (forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy)))))
% Found x10:=(x1 Xx):(forall (Xy0:fofType), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found x20:=(x2 Xx):(forall (Xy0:fofType), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))
% Found (x2 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found (x2 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found x10:=(x1 Xx):(forall (Xy0:fofType), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found x20:=(x2 Xx):(forall (Xy0:fofType), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))
% Found (x2 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found (x2 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found x4:((Xr Xx) Xw)
% Found (fun (x4:((Xr Xx) Xw))=> x4) as proof of ((Xr Xx) Xw)
% Found (fun (Xw:fofType) (x4:((Xr Xx) Xw))=> x4) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found (fun (Xw:fofType) (x4:((Xr Xx) Xw))=> x4) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xr Xx) Xw)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x1000:=(x100 x3):((Xp Xx) Xw)
% Found (x100 x3) as proof of ((Xp Xx) Xw)
% Found ((x10 Xw) x3) as proof of ((Xp Xx) Xw)
% Found (((x1 Xx) Xw) x3) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of ((Xp Xx) Xw)
% Found (fun (x3:((Xr Xx) Xw)) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (Xw:fofType) (x3:((Xr Xx) Xw)) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x3:((Xr Xx) Xw)) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))))
% 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:fofType) (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:fofType) (Xz:fofType) (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:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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 (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x10000:=(x1000 x2):((Xp Xx) Xw)
% Found (x1000 x2) as proof of ((Xp Xx) Xw)
% Found ((x100 Xw) x2) as proof of ((Xp Xx) Xw)
% Found (((x10 Xx) Xw) x2) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of ((Xp Xx) Xw)
% Found (fun (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x2:((Xr Xx) Xw)) (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw)) (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))))
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw)) (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))))
% Found x4:((Xr Xx) Xw)
% Found (fun (x4:((Xr Xx) Xw))=> x4) as proof of ((Xr Xx) Xw)
% Found (fun (Xw:fofType) (x4:((Xr Xx) Xw))=> x4) as proof of (((Xr Xx) Xw)->((Xr Xx) Xw))
% Found (fun (Xw:fofType) (x4:((Xr Xx) Xw))=> x4) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xr Xx) Xw)))
% Found x4:((Xr Xx0) Xy0)
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xy0))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xr Xx0) Xy0)))
% Found x2000:=(x200 x1):((Xp Xx) Xw)
% Found (x200 x1) as proof of ((Xp Xx) Xw)
% Found ((x20 Xw) x1) as proof of ((Xp Xx) Xw)
% Found (((x2 Xx) Xw) x1) as proof of ((Xp Xx) Xw)
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((Xp Xx) Xw)
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (and_rect00 (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found ((and_rect0 ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (fun (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of ((Xp Xx) Xw)
% Found (fun (x1:((Xr Xx) Xw)) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((Xr Xx) Xw)->(((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->(((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw))))
% Found x2000:=(x200 x1):((Xp Xx) Xw)
% Found (x200 x1) as proof of ((Xp Xx) Xw)
% Found ((x20 Xw) x1) as proof of ((Xp Xx) Xw)
% Found (((x2 Xx) Xw) x1) as proof of ((Xp Xx) Xw)
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((Xp Xx) Xw)
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (and_rect00 (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found ((and_rect0 ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (fun (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of ((Xp Xx) Xw)
% Found (fun (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw))
% Found (fun (x1:((Xr Xx) Xw)) (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((Xr Xx) Xw)->(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw))))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw)))))
% Found x1000:=(x100 x3):((Xp Xx) Xw)
% Found (x100 x3) as proof of ((Xp Xx) Xw)
% Found ((x10 Xw) x3) as proof of ((Xp Xx) Xw)
% Found (((x1 Xx) Xw) x3) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of ((Xp Xx) Xw)
% Found (fun (x3:((Xr Xx) Xw)) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (Xw:fofType) (x3:((Xr Xx) Xw)) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x3:((Xr Xx) Xw)) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x1 Xx) Xw) x3)) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))))
% 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:fofType) (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:fofType) (Xz:fofType) (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:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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 (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x3000:=(x300 x2):((Xp Xx) Xw)
% Found (x300 x2) as proof of ((Xp Xx) Xw)
% Found ((x30 Xw) x2) as proof of ((Xp Xx) Xw)
% Found (((x3 Xx) Xw) x2) as proof of ((Xp Xx) Xw)
% Found (fun (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)) as proof of ((Xp Xx) Xw)
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (and_rect00 (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2))) as proof of ((Xp Xx) Xw)
% Found ((and_rect0 ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2))) as proof of ((Xp Xx) Xw)
% Found (fun (x2:((Xr Xx) Xw))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)))) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)))) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found x10000:=(x1000 x2):((Xp Xx) Xw)
% Found (x1000 x2) as proof of ((Xp Xx) Xw)
% Found ((x100 Xw) x2) as proof of ((Xp Xx) Xw)
% Found (((x10 Xx) Xw) x2) as proof of ((Xp Xx) Xw)
% Found (fun (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of ((Xp Xx) Xw)
% Found (fun (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x2:((Xr Xx) Xw)) (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw)) (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))))
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw)) (x10:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x20:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x10 Xx) Xw) x2)) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))))
% Found x2000:=(x200 x1):((Xp Xx) Xw)
% Found (x200 x1) as proof of ((Xp Xx) Xw)
% Found ((x20 Xw) x1) as proof of ((Xp Xx) Xw)
% Found (((x2 Xx) Xw) x1) as proof of ((Xp Xx) Xw)
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((Xp Xx) Xw)
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (and_rect00 (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found ((and_rect0 ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (fun (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of ((Xp Xx) Xw)
% Found (fun (x1:((Xr Xx) Xw)) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((Xr Xx) Xw)->(((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->(((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((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:fofType) (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:fofType) (Xz:fofType) (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:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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 (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x2000:=(x200 x1):((Xp Xx) Xw)
% Found (x200 x1) as proof of ((Xp Xx) Xw)
% Found ((x20 Xw) x1) as proof of ((Xp Xx) Xw)
% Found (((x2 Xx) Xw) x1) as proof of ((Xp Xx) Xw)
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((Xp Xx) Xw)
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (and_rect00 (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found ((and_rect0 ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1))) as proof of ((Xp Xx) Xw)
% Found (fun (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of ((Xp Xx) Xw)
% Found (fun (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw))
% Found (fun (x1:((Xr Xx) Xw)) (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw)))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (((Xr Xx) Xw)->(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw))))
% Found (fun (Xw:fofType) (x1:((Xr Xx) Xw)) (Xp:(fofType->(fofType->Prop))) (x00:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x2:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x2) x00)) ((Xp Xx) Xw)) (fun (x2:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x3:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x2 Xx) Xw) x1)))) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xw)))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% 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:fofType) (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:fofType) (Xz:fofType) (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:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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 (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x3000:=(x300 x2):((Xp Xx) Xw)
% Found (x300 x2) as proof of ((Xp Xx) Xw)
% Found ((x30 Xw) x2) as proof of ((Xp Xx) Xw)
% Found (((x3 Xx) Xw) x2) as proof of ((Xp Xx) Xw)
% Found (fun (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)) as proof of ((Xp Xx) Xw)
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw))
% Found (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xw)))
% Found (and_rect00 (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2))) as proof of ((Xp Xx) Xw)
% Found ((and_rect0 ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2))) as proof of ((Xp Xx) Xw)
% Found (fun (x2:((Xr Xx) Xw))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)))) as proof of (((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (fun (Xw:fofType) (x2:((Xr Xx) Xw))=> (((fun (P:Type) (x3:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x3) x0)) ((Xp Xx) Xw)) (fun (x3:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x4:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> (((x3 Xx) Xw) x2)))) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x2 as proof of ((Xr Xv) Xy0)
% Found x50:=(x5 x20):(Xq Xz)
% Found (x5 x20) as proof of (Xq Xz)
% Found (fun (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (Xq Xz)
% Found (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->(Xq Xz))
% Found (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->(Xq Xz)))
% Found (and_rect10 (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (fun (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (Xq Xz)
% Found (fun (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))
% Found (fun (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xz:fofType), (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x3 as proof of ((Xr Xv) Xy0)
% 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:fofType) (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:fofType) (Xz:fofType) (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:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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 (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% 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:fofType) (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:fofType) (Xz:fofType) (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:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (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 (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and (Xq Xy0)) (Xq Xz))->(Xq Xz))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x10:=(x1 Xx):(forall (Xy0:fofType), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xy0) Xw)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xy0) Xw)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xy0) Xw)))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x2 as proof of ((Xr Xv) Xy0)
% Found x50:=(x5 x20):(Xq Xz)
% Found (x5 x20) as proof of (Xq Xz)
% Found (fun (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (Xq Xz)
% Found (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->(Xq Xz))
% Found (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)) as proof of (((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->(Xq Xz)))
% Found (and_rect10 (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found ((and_rect1 (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20))) as proof of (Xq Xz)
% Found (fun (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (Xq Xz)
% Found (fun (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))
% Found (fun (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xz:fofType), (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x3:((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))) (x20:(forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))=> (((fun (P:Type) (x4:(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))->(((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))->P)))=> (((((and_rect ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz))) P) x4) x3)) (Xq Xz)) (fun (x4:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) (x5:((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))=> (x5 x20)))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xy0))) ((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))->((forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw)))->(Xq Xz)))))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x3 as proof of ((Xr Xv) Xy0)
% Found x6:((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6) as proof of (((and (Xq Xv)) ((Xr Xv) Xz))->((and (Xq Xv)) ((Xr Xv) Xz)))
% Found (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6) as proof of (((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->((and (Xq Xv)) ((Xr Xv) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6)) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found ((and_rect1 ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6)) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6)) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz)))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv) Xy0))
% Found x100:=(x10 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x10 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xy0))
% Found ((x1 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xy0))
% Found ((x1 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xy0))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found x4 as proof of ((Xr Xv) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x10:=(x1 Xx):(forall (Xy0:fofType), (((Xr Xx) Xy0)->((Xp Xx) Xy0)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xy0) Xw)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xy0) Xw)))
% Found (x1 Xx) as proof of (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xy0) Xw)))
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x40:=(x4 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv) Xy0))
% Found x6:((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6) as proof of (((and (Xq Xv)) ((Xr Xv) Xz))->((and (Xq Xv)) ((Xr Xv) Xz)))
% Found (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6) as proof of (((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->((and (Xq Xv)) ((Xr Xv) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6)) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found ((and_rect1 ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6)) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6)) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of ((and (Xq Xv)) ((Xr Xv) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv)) ((Xr Xv) Xy0))->(((and (Xq Xv)) ((Xr Xv) Xz))->P)))=> (((((and_rect ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz))) P) x5) x4)) ((and (Xq Xv)) ((Xr Xv) Xz))) (fun (x5:((and (Xq Xv)) ((Xr Xv) Xy0))) (x6:((and (Xq Xv)) ((Xr Xv) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv)) ((Xr Xv) Xy0))) ((and (Xq Xv)) ((Xr Xv) Xz)))->((and (Xq Xv)) ((Xr Xv) Xz)))))
% Found x40:=(x4 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found x100:=(x10 Xw):(((Xr Xx) Xw)->((Xp Xx) Xw))
% Found (x10 Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xy0))
% Found ((x1 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xy0))
% Found ((x1 Xx) Xw) as proof of (((Xr Xx) Xw)->((Xp Xx) Xy0))
% Found x20:=(x2 x00):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x2 x00) as proof of ((Xp Xx) Xy0)
% Found (x2 x00) as proof of ((Xp Xx) Xy0)
% Found x40:=(x4 x00):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x00) as proof of ((Xp Xx) Xy0)
% Found (x4 x00) as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x1000:=(x100 x6):((Xp Xy0) Xw)
% Found (x100 x6) as proof of ((Xp Xy0) Xw)
% Found ((x10 Xw) x6) as proof of ((Xp Xy0) Xw)
% Found (((x1 Xy0) Xw) x6) as proof of ((Xp Xy0) Xw)
% Found (((x1 Xy0) Xw) x6) as proof of ((Xp Xy0) Xw)
% Found ((conj20 x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found (((conj2 ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found (x2000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found ((x200 Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found (((fun (Xy0:fofType)=> ((x20 Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of (((Xr Xv) Xw)->((Xp Xx) Xw))
% Found (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of (((Xp Xx) Xv)->(((Xr Xv) Xw)->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))
% Found (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (forall (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))
% Found (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))
% Found ((conj10 (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found (((conj1 (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found (x3 ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))) as proof of ((Xp Xx) Xy)
% Found ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xy))
% Found (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xy)))
% Found (and_rect00 (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found ((and_rect0 ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (Xp:(fofType->(fofType->Prop))) (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))
% Found (fun (x:(forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (Xp:(fofType->(fofType->Prop))) (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy)))
% Found (fun (x:(forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (Xp:(fofType->(fofType->Prop))) (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of ((forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))->(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x3 as proof of ((Xr Xv0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x6:((Xr Xv) Xz)
% Found (fun (x6:((Xr Xv) Xz))=> x6) as proof of ((Xr Xv) Xz)
% Found (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6) as proof of (((Xr Xv) Xz)->((Xr Xv) Xz))
% Found (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6) as proof of (((Xr Xv) Xy0)->(((Xr Xv) Xz)->((Xr Xv) Xz)))
% Found (and_rect10 (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found ((and_rect1 ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found (fun (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of ((Xr Xv) Xz)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (forall (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz))))
% Found x6:(Xq Xv)
% Found (fun (x6:(Xq Xv))=> x6) as proof of (Xq Xv)
% Found (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6) as proof of ((Xq Xv)->(Xq Xv))
% Found (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6) as proof of ((Xq Xv)->((Xq Xv)->(Xq Xv)))
% Found (and_rect10 (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6)) as proof of (Xq Xv)
% Found ((and_rect1 (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6)) as proof of (Xq Xv)
% Found (fun (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (Xq Xv)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (((and (Xq Xv)) (Xq Xv))->(Xq Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (fofType->(((and (Xq Xv)) (Xq Xv))->(Xq Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv)) (Xq Xv))->(Xq Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv)) (Xq Xv))->(Xq Xv)))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x2 as proof of ((Xr Xv0) Xv)
% Found x5:((Xr Xx0) Xv)
% Found (fun (x6:((Xr Xy0) Xv))=> x5) as proof of ((Xr Xx0) Xv)
% Found (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5) as proof of (((Xr Xy0) Xv)->((Xr Xx0) Xv))
% Found (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5) as proof of (((Xr Xx0) Xv)->(((Xr Xy0) Xv)->((Xr Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found ((and_rect1 ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found (fun (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of ((Xr Xx0) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))))
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x40:=(x4 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found x3:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x3 as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x40:=(x4 x20):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found (x4 x20) as proof of ((Xp Xx) Xy0)
% Found x20:=(x2 x00):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x2 x00) as proof of ((Xp Xx) Xy0)
% Found (x2 x00) as proof of ((Xp Xx) Xy0)
% Found x40:=(x4 x00):((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found (x4 x00) as proof of ((Xp Xx) Xy0)
% Found (x4 x00) as proof of ((Xp Xx) Xy0)
% Found x5:((Xp Xx) Xv)
% Instantiate: Xy0:=Xv:fofType
% Found x5 as proof of ((Xp Xx) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv)
% Found x1000:=(x100 x6):((Xp Xy0) Xw)
% Found (x100 x6) as proof of ((Xp Xy0) Xw)
% Found ((x10 Xw) x6) as proof of ((Xp Xy0) Xw)
% Found (((x1 Xy0) Xw) x6) as proof of ((Xp Xy0) Xw)
% Found (((x1 Xy0) Xw) x6) as proof of ((Xp Xy0) Xw)
% Found ((conj20 x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found (((conj2 ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xw))
% Found (x2000 ((((conj ((Xp Xx) Xy0)) ((Xp Xy0) Xw)) x5) (((x1 Xy0) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found ((x200 Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found (((fun (Xy0:fofType)=> ((x20 Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))) as proof of ((Xp Xx) Xw)
% Found (fun (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of ((Xp Xx) Xw)
% Found (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of (((Xr Xv) Xw)->((Xp Xx) Xw))
% Found (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))) as proof of (((Xp Xx) Xv)->(((Xr Xv) Xw)->((Xp Xx) Xw)))
% Found (and_rect10 (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xx) Xw)
% Found ((and_rect1 ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xx) Xw)
% Found (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))) as proof of ((Xp Xx) Xw)
% Found (fun (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of ((Xp Xx) Xw)
% Found (fun (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))
% Found (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (forall (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))
% Found (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))) as proof of (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))
% Found ((conj10 (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found (((conj1 (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))) as proof of ((and (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw))))
% Found (x3 ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))) as proof of ((Xp Xx) Xy)
% Found ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xy))
% Found (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))) as proof of ((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->((Xp Xx) Xy)))
% Found (and_rect00 (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found ((and_rect0 ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6)))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of ((Xp Xx) Xy)
% Found (fun (Xp:(fofType->(fofType->Prop))) (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))
% Found (fun (x:(forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (Xp:(fofType->(fofType->Prop))) (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of (forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy)))
% Found (fun (x:(forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))) (Xp:(fofType->(fofType->Prop))) (x0:((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))))=> (((fun (P:Type) (x1:((forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))->((forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))->P)))=> (((((and_rect (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))) P) x1) x0)) ((Xp Xx) Xy)) (fun (x1:(forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (x2:(forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))=> ((x (Xp Xx)) ((((conj (forall (Xw:fofType), (((Xr Xx) Xw)->((Xp Xx) Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and ((Xp Xx) Xv)) ((Xr Xv) Xw))->((Xp Xx) Xw)))) (x1 Xx)) (fun (Xv:fofType) (Xw:fofType) (x4:((and ((Xp Xx) Xv)) ((Xr Xv) Xw)))=> (((fun (P:Type) (x5:(((Xp Xx) Xv)->(((Xr Xv) Xw)->P)))=> (((((and_rect ((Xp Xx) Xv)) ((Xr Xv) Xw)) P) x5) x4)) ((Xp Xx) Xw)) (fun (x5:((Xp Xx) Xv)) (x6:((Xr Xv) Xw))=> (((fun (Xy0:fofType)=> (((x2 Xx) Xy0) Xw)) Xv) ((((conj ((Xp Xx) Xv)) ((Xp Xv) Xw)) x5) (((x1 Xv) Xw) x6))))))))))) as proof of ((forall (Xq:(fofType->Prop)), (((and (forall (Xw:fofType), (((Xr Xx) Xw)->(Xq Xw)))) (forall (Xv:fofType) (Xw:fofType), (((and (Xq Xv)) ((Xr Xv) Xw))->(Xq Xw))))->(Xq Xy)))->(forall (Xp:(fofType->(fofType->Prop))), (((and (forall (Xx0:fofType) (Xy0:fofType), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:fofType) (Xy0:fofType) (Xz:fofType), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))->((Xp Xx) Xy))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x3 as proof of ((Xr Xv0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x6:((Xr Xv) Xz)
% Found (fun (x6:((Xr Xv) Xz))=> x6) as proof of ((Xr Xv) Xz)
% Found (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6) as proof of (((Xr Xv) Xz)->((Xr Xv) Xz))
% Found (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6) as proof of (((Xr Xv) Xy0)->(((Xr Xv) Xz)->((Xr Xv) Xz)))
% Found (and_rect10 (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found ((and_rect1 ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6)) as proof of ((Xr Xv) Xz)
% Found (fun (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of ((Xr Xv) Xz)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (forall (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv) Xy0)) ((Xr Xv) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv) Xy0)->(((Xr Xv) Xz)->P)))=> (((((and_rect ((Xr Xv) Xy0)) ((Xr Xv) Xz)) P) x5) x4)) ((Xr Xv) Xz)) (fun (x5:((Xr Xv) Xy0)) (x6:((Xr Xv) Xz))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv) Xy0)) ((Xr Xv) Xz))->((Xr Xv) Xz))))
% Found x6:(Xq Xv)
% Found (fun (x6:(Xq Xv))=> x6) as proof of (Xq Xv)
% Found (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6) as proof of ((Xq Xv)->(Xq Xv))
% Found (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6) as proof of ((Xq Xv)->((Xq Xv)->(Xq Xv)))
% Found (and_rect10 (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6)) as proof of (Xq Xv)
% Found ((and_rect1 (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6)) as proof of (Xq Xv)
% Found (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6)) as proof of (Xq Xv)
% Found (fun (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (Xq Xv)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (((and (Xq Xv)) (Xq Xv))->(Xq Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (fofType->(((and (Xq Xv)) (Xq Xv))->(Xq Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv)) (Xq Xv))->(Xq Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv)) (Xq Xv)))=> (((fun (P:Type) (x5:((Xq Xv)->((Xq Xv)->P)))=> (((((and_rect (Xq Xv)) (Xq Xv)) P) x5) x4)) (Xq Xv)) (fun (x5:(Xq Xv)) (x6:(Xq Xv))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv)) (Xq Xv))->(Xq Xv)))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x2 as proof of ((Xr Xv0) Xv)
% Found x5:((Xr Xx0) Xv)
% Found (fun (x6:((Xr Xy0) Xv))=> x5) as proof of ((Xr Xx0) Xv)
% Found (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5) as proof of (((Xr Xy0) Xv)->((Xr Xx0) Xv))
% Found (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5) as proof of (((Xr Xx0) Xv)->(((Xr Xy0) Xv)->((Xr Xx0) Xv)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found ((and_rect1 ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5)) as proof of ((Xr Xx0) Xv)
% Found (fun (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of ((Xr Xx0) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv)->(((Xr Xy0) Xv)->P)))=> (((((and_rect ((Xr Xx0) Xv)) ((Xr Xy0) Xv)) P) x5) x4)) ((Xr Xx0) Xv)) (fun (x5:((Xr Xx0) Xv)) (x6:((Xr Xy0) Xv))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv)) ((Xr Xy0) Xv))->((Xr Xx0) Xv))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv0) Xv)
% Found x6:((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xv))->((and (Xq Xv0)) ((Xr Xv0) Xv)))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->((and (Xq Xv0)) ((Xr Xv0) Xv))))
% Found (and_rect10 (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found ((and_rect1 ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv))))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found x4 as proof of ((Xr Xv0) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType;Xv:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv0) Xv)
% Found x6:((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xv))->((and (Xq Xv0)) ((Xr Xv0) Xv)))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->((and (Xq Xv0)) ((Xr Xv0) Xv))))
% Found (and_rect10 (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found ((and_rect1 ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xv))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xv))->(((and (Xq Xv0)) ((Xr Xv0) Xv))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xv))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xv))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xv)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv0)) ((Xr Xv0) Xv))) ((and (Xq Xv0)) ((Xr Xv0) Xv)))->((and (Xq Xv0)) ((Xr Xv0) Xv))))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x3 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x4 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x4 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x2 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x6:((Xr Xv0) Xv)
% Found (fun (x6:((Xr Xv0) Xv))=> x6) as proof of ((Xr Xv0) Xv)
% Found (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6) as proof of (((Xr Xv0) Xv)->((Xr Xv0) Xv))
% Found (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6) as proof of (((Xr Xv0) Xv)->(((Xr Xv0) Xv)->((Xr Xv0) Xv)))
% Found (and_rect10 (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6)) as proof of ((Xr Xv0) Xv)
% Found ((and_rect1 ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6)) as proof of ((Xr Xv0) Xv)
% Found (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6)) as proof of ((Xr Xv0) Xv)
% Found (fun (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of ((Xr Xv0) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (fofType->(((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv)))))
% Found x6:(Xq Xv0)
% Found (fun (x6:(Xq Xv0))=> x6) as proof of (Xq Xv0)
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->(Xq Xv0))
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->((Xq Xv0)->(Xq Xv0)))
% Found (and_rect10 (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found ((and_rect1 (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (fun (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (Xq Xv0)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x3 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x4 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x4 as proof of ((Xr Xv0) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x2 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x6:((Xr Xv0) Xv)
% Found (fun (x6:((Xr Xv0) Xv))=> x6) as proof of ((Xr Xv0) Xv)
% Found (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6) as proof of (((Xr Xv0) Xv)->((Xr Xv0) Xv))
% Found (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6) as proof of (((Xr Xv0) Xv)->(((Xr Xv0) Xv)->((Xr Xv0) Xv)))
% Found (and_rect10 (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6)) as proof of ((Xr Xv0) Xv)
% Found ((and_rect1 ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6)) as proof of ((Xr Xv0) Xv)
% Found (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6)) as proof of ((Xr Xv0) Xv)
% Found (fun (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of ((Xr Xv0) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (fofType->(((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xv)->(((Xr Xv0) Xv)->P)))=> (((((and_rect ((Xr Xv0) Xv)) ((Xr Xv0) Xv)) P) x5) x4)) ((Xr Xv0) Xv)) (fun (x5:((Xr Xv0) Xv)) (x6:((Xr Xv0) Xv))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv0) Xv)) ((Xr Xv0) Xv))->((Xr Xv0) Xv)))))
% Found x6:(Xq Xv0)
% Found (fun (x6:(Xq Xv0))=> x6) as proof of (Xq Xv0)
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->(Xq Xv0))
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->((Xq Xv0)->(Xq Xv0)))
% Found (and_rect10 (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found ((and_rect1 (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (fun (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (Xq Xv0)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv0)
% Found x5:((Xr Xx0) Xv0)
% Found (fun (x6:((Xr Xy0) Xv0))=> x5) as proof of ((Xr Xx0) Xv0)
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xy0) Xv0)->((Xr Xx0) Xv0))
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->((Xr Xx0) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found ((and_rect1 ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (fun (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of ((Xr Xx0) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x5:((Xr Xx0) Xv0)
% Found (fun (x6:((Xr Xy0) Xv0))=> x5) as proof of ((Xr Xx0) Xv0)
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xy0) Xv0)->((Xr Xx0) Xv0))
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->((Xr Xx0) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found ((and_rect1 ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (fun (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of ((Xr Xx0) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x4 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv0) Xy0))
% Found x6:((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xz))->((and (Xq Xv0)) ((Xr Xv0) Xz)))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->((and (Xq Xv0)) ((Xr Xv0) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found ((and_rect1 ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz)))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found x4 as proof of ((Xr Xv0) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv0) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv0) Xy0))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x6:((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xz))->((and (Xq Xv0)) ((Xr Xv0) Xz)))
% Found (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6) as proof of (((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->((and (Xq Xv0)) ((Xr Xv0) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found ((and_rect1 ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6)) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of ((and (Xq Xv0)) ((Xr Xv0) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv0)) ((Xr Xv0) Xy0))->(((and (Xq Xv0)) ((Xr Xv0) Xz))->P)))=> (((((and_rect ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz))) P) x5) x4)) ((and (Xq Xv0)) ((Xr Xv0) Xz))) (fun (x5:((and (Xq Xv0)) ((Xr Xv0) Xy0))) (x6:((and (Xq Xv0)) ((Xr Xv0) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv0)) ((Xr Xv0) Xy0))) ((and (Xq Xv0)) ((Xr Xv0) Xz)))->((and (Xq Xv0)) ((Xr Xv0) Xz)))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x2 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x6:((Xr Xv0) Xz)
% Found (fun (x6:((Xr Xv0) Xz))=> x6) as proof of ((Xr Xv0) Xz)
% Found (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6) as proof of (((Xr Xv0) Xz)->((Xr Xv0) Xz))
% Found (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6) as proof of (((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->((Xr Xv0) Xz)))
% Found (and_rect10 (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6)) as proof of ((Xr Xv0) Xz)
% Found ((and_rect1 ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6)) as proof of ((Xr Xv0) Xz)
% Found (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6)) as proof of ((Xr Xv0) Xz)
% Found (fun (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of ((Xr Xv0) Xz)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (forall (Xz:fofType), (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz))))
% Found x6:(Xq Xv0)
% Found (fun (x6:(Xq Xv0))=> x6) as proof of (Xq Xv0)
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->(Xq Xv0))
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->((Xq Xv0)->(Xq Xv0)))
% Found (and_rect10 (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found ((and_rect1 (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (fun (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (Xq Xv0)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x2 as proof of ((Xr Xv1) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x2 as proof of ((Xr Xv1) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x6:((Xr Xv0) Xz)
% Found (fun (x6:((Xr Xv0) Xz))=> x6) as proof of ((Xr Xv0) Xz)
% Found (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6) as proof of (((Xr Xv0) Xz)->((Xr Xv0) Xz))
% Found (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6) as proof of (((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->((Xr Xv0) Xz)))
% Found (and_rect10 (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6)) as proof of ((Xr Xv0) Xz)
% Found ((and_rect1 ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6)) as proof of ((Xr Xv0) Xz)
% Found (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6)) as proof of ((Xr Xv0) Xz)
% Found (fun (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of ((Xr Xv0) Xz)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (forall (Xz:fofType), (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv0) Xy0)->(((Xr Xv0) Xz)->P)))=> (((((and_rect ((Xr Xv0) Xy0)) ((Xr Xv0) Xz)) P) x5) x4)) ((Xr Xv0) Xz)) (fun (x5:((Xr Xv0) Xy0)) (x6:((Xr Xv0) Xz))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv0) Xy0)) ((Xr Xv0) Xz))->((Xr Xv0) Xz))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x6:(Xq Xv0)
% Found (fun (x6:(Xq Xv0))=> x6) as proof of (Xq Xv0)
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->(Xq Xv0))
% Found (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6) as proof of ((Xq Xv0)->((Xq Xv0)->(Xq Xv0)))
% Found (and_rect10 (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found ((and_rect1 (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6)) as proof of (Xq Xv0)
% Found (fun (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (Xq Xv0)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv0)) (Xq Xv0)))=> (((fun (P:Type) (x5:((Xq Xv0)->((Xq Xv0)->P)))=> (((((and_rect (Xq Xv0)) (Xq Xv0)) P) x5) x4)) (Xq Xv0)) (fun (x5:(Xq Xv0)) (x6:(Xq Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv0)) (Xq Xv0))->(Xq Xv0)))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x2 as proof of ((Xr Xv1) Xy0)
% Found x5:((Xr Xx0) Xv0)
% Found (fun (x6:((Xr Xy0) Xv0))=> x5) as proof of ((Xr Xx0) Xv0)
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xy0) Xv0)->((Xr Xx0) Xv0))
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->((Xr Xx0) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found ((and_rect1 ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (fun (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of ((Xr Xx0) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x5:((Xr Xx0) Xv0)
% Found (fun (x6:((Xr Xy0) Xv0))=> x5) as proof of ((Xr Xx0) Xv0)
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xy0) Xv0)->((Xr Xx0) Xv0))
% Found (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5) as proof of (((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->((Xr Xx0) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found ((and_rect1 ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5)) as proof of ((Xr Xx0) Xv0)
% Found (fun (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of ((Xr Xx0) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv0)->(((Xr Xy0) Xv0)->P)))=> (((((and_rect ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0)) P) x5) x4)) ((Xr Xx0) Xv0)) (fun (x5:((Xr Xx0) Xv0)) (x6:((Xr Xy0) Xv0))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv0)) ((Xr Xy0) Xv0))->((Xr Xx0) Xv0))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x6:((Xr Xv1) Xv0)
% Found (fun (x6:((Xr Xv1) Xv0))=> x6) as proof of ((Xr Xv1) Xv0)
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->((Xr Xv1) Xv0))
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->((Xr Xv1) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found ((and_rect1 ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (fun (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of ((Xr Xv1) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))))
% Found x6:(Xq Xv1)
% Found (fun (x6:(Xq Xv1))=> x6) as proof of (Xq Xv1)
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->(Xq Xv1))
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->((Xq Xv1)->(Xq Xv1)))
% Found (and_rect10 (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found ((and_rect1 (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (fun (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (Xq Xv1)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x6:((Xr Xv1) Xv0)
% Found (fun (x6:((Xr Xv1) Xv0))=> x6) as proof of ((Xr Xv1) Xv0)
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->((Xr Xv1) Xv0))
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->((Xr Xv1) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found ((and_rect1 ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (fun (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of ((Xr Xv1) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))))
% Found x6:(Xq Xv1)
% Found (fun (x6:(Xq Xv1))=> x6) as proof of (Xq Xv1)
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->(Xq Xv1))
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->((Xq Xv1)->(Xq Xv1)))
% Found (and_rect10 (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found ((and_rect1 (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (fun (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (Xq Xv1)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x5:((Xr Xx0) Xv1)
% Found (fun (x6:((Xr Xy0) Xv1))=> x5) as proof of ((Xr Xx0) Xv1)
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xy0) Xv1)->((Xr Xx0) Xv1))
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->((Xr Xx0) Xv1)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found ((and_rect1 ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (fun (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of ((Xr Xx0) Xv1)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv1) Xy0))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x2 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))))
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))))
% Found x6:((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6) as proof of (((and (Xq Xv00)) ((Xr Xv00) Xv))->((and (Xq Xv00)) ((Xr Xv00) Xv)))
% Found (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6) as proof of (((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->((and (Xq Xv00)) ((Xr Xv00) Xv))))
% Found (and_rect10 (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6)) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found ((and_rect1 ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6)) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6)) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv))))))
% Found x5:((Xr Xx0) Xv1)
% Found (fun (x6:((Xr Xy0) Xv1))=> x5) as proof of ((Xr Xx0) Xv1)
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xy0) Xv1)->((Xr Xx0) Xv1))
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->((Xr Xx0) Xv1)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found ((and_rect1 ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (fun (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of ((Xr Xx0) Xv1)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv0:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xv0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv1) Xy0))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x2 as proof of ((Xr Xv1) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))))
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xv0))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xv0))->(((and (Xq Xv1)) ((Xr Xv1) Xv0))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xv0))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xv0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xv0)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv1)) ((Xr Xv1) Xv0))) ((and (Xq Xv1)) ((Xr Xv1) Xv0)))->((and (Xq Xv1)) ((Xr Xv1) Xv0))))))
% Found x6:((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6) as proof of (((and (Xq Xv00)) ((Xr Xv00) Xv))->((and (Xq Xv00)) ((Xr Xv00) Xv)))
% Found (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6) as proof of (((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->((and (Xq Xv00)) ((Xr Xv00) Xv))))
% Found (and_rect10 (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6)) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found ((and_rect1 ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6)) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6)) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of ((and (Xq Xv00)) ((Xr Xv00) Xv))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))))=> (((fun (P:Type) (x5:(((and (Xq Xv00)) ((Xr Xv00) Xv))->(((and (Xq Xv00)) ((Xr Xv00) Xv))->P)))=> (((((and_rect ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv))) P) x5) x4)) ((and (Xq Xv00)) ((Xr Xv00) Xv))) (fun (x5:((and (Xq Xv00)) ((Xr Xv00) Xv))) (x6:((and (Xq Xv00)) ((Xr Xv00) Xv)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv00)) ((Xr Xv00) Xv))) ((and (Xq Xv00)) ((Xr Xv00) Xv)))->((and (Xq Xv00)) ((Xr Xv00) Xv))))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x3 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv00)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x2 as proof of ((Xr Xv00) Xv)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv00)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x3 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv00)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x2 as proof of ((Xr Xv00) Xv)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x6:((Xr Xv1) Xv0)
% Found (fun (x6:((Xr Xv1) Xv0))=> x6) as proof of ((Xr Xv1) Xv0)
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->((Xr Xv1) Xv0))
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->((Xr Xv1) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found ((and_rect1 ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (fun (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of ((Xr Xv1) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))))
% Found x6:((Xr Xv00) Xv)
% Found (fun (x6:((Xr Xv00) Xv))=> x6) as proof of ((Xr Xv00) Xv)
% Found (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6) as proof of (((Xr Xv00) Xv)->((Xr Xv00) Xv))
% Found (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6) as proof of (((Xr Xv00) Xv)->(((Xr Xv00) Xv)->((Xr Xv00) Xv)))
% Found (and_rect10 (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6)) as proof of ((Xr Xv00) Xv)
% Found ((and_rect1 ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6)) as proof of ((Xr Xv00) Xv)
% Found (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6)) as proof of ((Xr Xv00) Xv)
% Found (fun (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of ((Xr Xv00) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (fofType->(((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv)))))
% Found x6:((Xr Xv1) Xz)
% Found (fun (x6:((Xr Xv1) Xz))=> x6) as proof of ((Xr Xv1) Xz)
% Found (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6) as proof of (((Xr Xv1) Xz)->((Xr Xv1) Xz))
% Found (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6) as proof of (((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->((Xr Xv1) Xz)))
% Found (and_rect10 (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6)) as proof of ((Xr Xv1) Xz)
% Found ((and_rect1 ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6)) as proof of ((Xr Xv1) Xz)
% Found (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6)) as proof of ((Xr Xv1) Xz)
% Found (fun (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of ((Xr Xv1) Xz)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (forall (Xz:fofType), (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x6:(Xq Xv1)
% Found (fun (x6:(Xq Xv1))=> x6) as proof of (Xq Xv1)
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->(Xq Xv1))
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->((Xq Xv1)->(Xq Xv1)))
% Found (and_rect10 (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found ((and_rect1 (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (fun (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (Xq Xv1)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))))
% Found x6:(Xq Xv00)
% Found (fun (x6:(Xq Xv00))=> x6) as proof of (Xq Xv00)
% Found (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6) as proof of ((Xq Xv00)->(Xq Xv00))
% Found (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6) as proof of ((Xq Xv00)->((Xq Xv00)->(Xq Xv00)))
% Found (and_rect10 (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6)) as proof of (Xq Xv00)
% Found ((and_rect1 (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6)) as proof of (Xq Xv00)
% Found (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6)) as proof of (Xq Xv00)
% Found (fun (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (Xq Xv00)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (fofType->(((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00)))))
% Found x6:(Xq Xv1)
% Found (fun (x6:(Xq Xv1))=> x6) as proof of (Xq Xv1)
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->(Xq Xv1))
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->((Xq Xv1)->(Xq Xv1)))
% Found (and_rect10 (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found ((and_rect1 (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (fun (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (Xq Xv1)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x3 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x6:((Xr Xv00) Xv)
% Found (fun (x6:((Xr Xv00) Xv))=> x6) as proof of ((Xr Xv00) Xv)
% Found (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6) as proof of (((Xr Xv00) Xv)->((Xr Xv00) Xv))
% Found (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6) as proof of (((Xr Xv00) Xv)->(((Xr Xv00) Xv)->((Xr Xv00) Xv)))
% Found (and_rect10 (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6)) as proof of ((Xr Xv00) Xv)
% Found ((and_rect1 ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6)) as proof of ((Xr Xv00) Xv)
% Found (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6)) as proof of ((Xr Xv00) Xv)
% Found (fun (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of ((Xr Xv00) Xv)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (fofType->(((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv)))=> (((fun (P:Type) (x5:(((Xr Xv00) Xv)->(((Xr Xv00) Xv)->P)))=> (((((and_rect ((Xr Xv00) Xv)) ((Xr Xv00) Xv)) P) x5) x4)) ((Xr Xv00) Xv)) (fun (x5:((Xr Xv00) Xv)) (x6:((Xr Xv00) Xv))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv00) Xv)) ((Xr Xv00) Xv))->((Xr Xv00) Xv)))))
% Found x6:((Xr Xv1) Xv0)
% Found (fun (x6:((Xr Xv1) Xv0))=> x6) as proof of ((Xr Xv1) Xv0)
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->((Xr Xv1) Xv0))
% Found (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6) as proof of (((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->((Xr Xv1) Xv0)))
% Found (and_rect10 (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found ((and_rect1 ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6)) as proof of ((Xr Xv1) Xv0)
% Found (fun (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of ((Xr Xv1) Xv0)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xv0)->(((Xr Xv1) Xv0)->P)))=> (((((and_rect ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0)) P) x5) x4)) ((Xr Xv1) Xv0)) (fun (x5:((Xr Xv1) Xv0)) (x6:((Xr Xv1) Xv0))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((Xr Xv1) Xv0)) ((Xr Xv1) Xv0))->((Xr Xv1) Xv0)))))
% Found x6:((Xr Xv1) Xz)
% Found (fun (x6:((Xr Xv1) Xz))=> x6) as proof of ((Xr Xv1) Xz)
% Found (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6) as proof of (((Xr Xv1) Xz)->((Xr Xv1) Xz))
% Found (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6) as proof of (((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->((Xr Xv1) Xz)))
% Found (and_rect10 (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6)) as proof of ((Xr Xv1) Xz)
% Found ((and_rect1 ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6)) as proof of ((Xr Xv1) Xz)
% Found (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6)) as proof of ((Xr Xv1) Xz)
% Found (fun (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of ((Xr Xv1) Xz)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (forall (Xz:fofType), (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)))=> (((fun (P:Type) (x5:(((Xr Xv1) Xy0)->(((Xr Xv1) Xz)->P)))=> (((((and_rect ((Xr Xv1) Xy0)) ((Xr Xv1) Xz)) P) x5) x4)) ((Xr Xv1) Xz)) (fun (x5:((Xr Xv1) Xy0)) (x6:((Xr Xv1) Xz))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((Xr Xv1) Xy0)) ((Xr Xv1) Xz))->((Xr Xv1) Xz))))
% Found x6:(Xq Xv1)
% Found (fun (x6:(Xq Xv1))=> x6) as proof of (Xq Xv1)
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->(Xq Xv1))
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->((Xq Xv1)->(Xq Xv1)))
% Found (and_rect10 (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found ((and_rect1 (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (fun (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (Xq Xv1)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))))
% Found x6:(Xq Xv00)
% Found (fun (x6:(Xq Xv00))=> x6) as proof of (Xq Xv00)
% Found (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6) as proof of ((Xq Xv00)->(Xq Xv00))
% Found (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6) as proof of ((Xq Xv00)->((Xq Xv00)->(Xq Xv00)))
% Found (and_rect10 (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6)) as proof of (Xq Xv00)
% Found ((and_rect1 (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6)) as proof of (Xq Xv00)
% Found (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6)) as proof of (Xq Xv00)
% Found (fun (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (Xq Xv00)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (fofType->(((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv00)) (Xq Xv00)))=> (((fun (P:Type) (x5:((Xq Xv00)->((Xq Xv00)->P)))=> (((((and_rect (Xq Xv00)) (Xq Xv00)) P) x5) x4)) (Xq Xv00)) (fun (x5:(Xq Xv00)) (x6:(Xq Xv00))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv00)) (Xq Xv00))->(Xq Xv00)))))
% Found x6:(Xq Xv1)
% Found (fun (x6:(Xq Xv1))=> x6) as proof of (Xq Xv1)
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->(Xq Xv1))
% Found (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6) as proof of ((Xq Xv1)->((Xq Xv1)->(Xq Xv1)))
% Found (and_rect10 (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found ((and_rect1 (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6)) as proof of (Xq Xv1)
% Found (fun (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (Xq Xv1)
% Found (fun (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and (Xq Xv1)) (Xq Xv1)))=> (((fun (P:Type) (x5:((Xq Xv1)->((Xq Xv1)->P)))=> (((((and_rect (Xq Xv1)) (Xq Xv1)) P) x5) x4)) (Xq Xv1)) (fun (x5:(Xq Xv1)) (x6:(Xq Xv1))=> x6))) as proof of (fofType->(fofType->(fofType->(((and (Xq Xv1)) (Xq Xv1))->(Xq Xv1)))))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x2 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x6:((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6) as proof of (((and (Xq Xv2)) ((Xr Xv2) Xv1))->((and (Xq Xv2)) ((Xr Xv2) Xv1)))
% Found (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6) as proof of (((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->((and (Xq Xv2)) ((Xr Xv2) Xv1))))
% Found (and_rect10 (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6)) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found ((and_rect1 ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6)) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6)) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1))))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x5:((Xr Xx0) Xv1)
% Found (fun (x6:((Xr Xy0) Xv1))=> x5) as proof of ((Xr Xx0) Xv1)
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xy0) Xv1)->((Xr Xx0) Xv1))
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->((Xr Xx0) Xv1)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found ((and_rect1 ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (fun (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of ((Xr Xx0) Xv1)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found x5:((Xr Xx0) Xv00)
% Found (fun (x6:((Xr Xy0) Xv00))=> x5) as proof of ((Xr Xx0) Xv00)
% Found (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5) as proof of (((Xr Xy0) Xv00)->((Xr Xx0) Xv00))
% Found (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5) as proof of (((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->((Xr Xx0) Xv00)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5)) as proof of ((Xr Xx0) Xv00)
% Found ((and_rect1 ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5)) as proof of ((Xr Xx0) Xv00)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5)) as proof of ((Xr Xx0) Xv00)
% Found (fun (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of ((Xr Xx0) Xv00)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00))))
% Found x5:((Xr Xx0) Xv1)
% Found (fun (x6:((Xr Xy0) Xv1))=> x5) as proof of ((Xr Xx0) Xv1)
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xy0) Xv1)->((Xr Xx0) Xv1))
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->((Xr Xx0) Xv1)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found ((and_rect1 ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (fun (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of ((Xr Xx0) Xv1)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv1) Xy0))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv2)
% Found x6:((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6) as proof of (((and (Xq Xv2)) ((Xr Xv2) Xv1))->((and (Xq Xv2)) ((Xr Xv2) Xv1)))
% Found (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6) as proof of (((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->((and (Xq Xv2)) ((Xr Xv2) Xv1))))
% Found (and_rect10 (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6)) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found ((and_rect1 ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6)) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6)) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of ((and (Xq Xv2)) ((Xr Xv2) Xv1))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (fofType->(((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (fofType->(fofType->(((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1)))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))))=> (((fun (P:Type) (x5:(((and (Xq Xv2)) ((Xr Xv2) Xv1))->(((and (Xq Xv2)) ((Xr Xv2) Xv1))->P)))=> (((((and_rect ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) P) x5) x4)) ((and (Xq Xv2)) ((Xr Xv2) Xv1))) (fun (x5:((and (Xq Xv2)) ((Xr Xv2) Xv1))) (x6:((and (Xq Xv2)) ((Xr Xv2) Xv1)))=> x6))) as proof of (fofType->(fofType->(fofType->(((and ((and (Xq Xv2)) ((Xr Xv2) Xv1))) ((and (Xq Xv2)) ((Xr Xv2) Xv1)))->((and (Xq Xv2)) ((Xr Xv2) Xv1))))))
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x5:((Xr Xx0) Xv00)
% Found (fun (x6:((Xr Xy0) Xv00))=> x5) as proof of ((Xr Xx0) Xv00)
% Found (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5) as proof of (((Xr Xy0) Xv00)->((Xr Xx0) Xv00))
% Found (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5) as proof of (((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->((Xr Xx0) Xv00)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5)) as proof of ((Xr Xx0) Xv00)
% Found ((and_rect1 ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5)) as proof of ((Xr Xx0) Xv00)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5)) as proof of ((Xr Xx0) Xv00)
% Found (fun (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of ((Xr Xx0) Xv00)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv00)->(((Xr Xy0) Xv00)->P)))=> (((((and_rect ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00)) P) x5) x4)) ((Xr Xx0) Xv00)) (fun (x5:((Xr Xx0) Xv00)) (x6:((Xr Xy0) Xv00))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv00)) ((Xr Xy0) Xv00))->((Xr Xx0) Xv00))))
% Found x5:((Xr Xx0) Xv1)
% Found (fun (x6:((Xr Xy0) Xv1))=> x5) as proof of ((Xr Xx0) Xv1)
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xy0) Xv1)->((Xr Xx0) Xv1))
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->((Xr Xx0) Xv1)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found ((and_rect1 ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (fun (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of ((Xr Xx0) Xv1)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found x5:((Xr Xx0) Xv1)
% Found (fun (x6:((Xr Xy0) Xv1))=> x5) as proof of ((Xr Xx0) Xv1)
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xy0) Xv1)->((Xr Xx0) Xv1))
% Found (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5) as proof of (((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->((Xr Xx0) Xv1)))
% Found (and_rect10 (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found ((and_rect1 ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5)) as proof of ((Xr Xx0) Xv1)
% Found (fun (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of ((Xr Xx0) Xv1)
% Found (fun (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1)))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xv1)->(((Xr Xy0) Xv1)->P)))=> (((((and_rect ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1)) P) x5) x4)) ((Xr Xx0) Xv1)) (fun (x5:((Xr Xx0) Xv1)) (x6:((Xr Xy0) Xv1))=> x5))) as proof of (forall (Xx0:fofType) (Xy0:fofType), (fofType->(((and ((Xr Xx0) Xv1)) ((Xr Xy0) Xv1))->((Xr Xx0) Xv1))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv00:=Xx0:fofType
% Found x4 as proof of ((Xr Xv00) Xv)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xv1) Xy0)
% Found (fun (Xy0:fofType) (x4:((Xr Xx0) Xy0))=> x4) as proof of (((Xr Xx0) Xy0)->((Xr Xv1) Xy0))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv2)
% Found x6:((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6) as proof of (((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (and_rect10 (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found ((and_rect1 ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6)) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of ((and (Xq Xv1)) ((Xr Xv1) Xz))
% Found (fun (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))
% Found (fun (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz))))
% Found (fun (Xx0:fofType) (Xy0:fofType) (Xz:fofType) (x4:((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))))=> (((fun (P:Type) (x5:(((and (Xq Xv1)) ((Xr Xv1) Xy0))->(((and (Xq Xv1)) ((Xr Xv1) Xz))->P)))=> (((((and_rect ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz))) P) x5) x4)) ((and (Xq Xv1)) ((Xr Xv1) Xz))) (fun (x5:((and (Xq Xv1)) ((Xr Xv1) Xy0))) (x6:((and (Xq Xv1)) ((Xr Xv1) Xz)))=> x6))) as proof of (fofType->(forall (Xy0:fofType) (Xz:fofType), (((and ((and (Xq Xv1)) ((Xr Xv1) Xy0))) ((and (Xq Xv1)) ((Xr Xv1) Xz)))->((and (Xq Xv1)) ((Xr Xv1) Xz)))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x3 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x2 as proof of ((Xr Xv3) Xv2)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv3:=Xx0:fofType;Xv2:=Xy0:fofType
% Found x4 as proof of ((Xr Xv3) Xv2)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x2 as proof of ((Xr Xv1) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType
% Found (fun (x4:((Xr Xx0) Xy0))=> x4) as proof of ((Xr Xx0) Xv1)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x2:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x2 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x3 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType
% Found x4 as proof of ((Xr Xv1) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xx0:fofType;Xv00:=Xy0:fofType
% Found x4 as proof of ((Xr Xv1) Xv00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xv1:=Xy0:fofType;Xv2:=Xx0:fofType
% Found x4 as proof of ((Xr Xv2) Xv1)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xv2:=Xx0:fofType
% Found x3 as proof of ((Xr Xv2) Xy0)
% Found x4:((Xr Xx0
% EOF
%------------------------------------------------------------------------------