%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU993^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n118.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 13:33:29 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU993^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n118.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 11:48:41 CDT 2014
% % CPUTime  : 300.01 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1b03560>, <kernel.Type object at 0x1b03320>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1b03518>, <kernel.Type object at 0x17468c0>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1b033b0>, <kernel.DependentProduct object at 0x1b777a0>) of role type named cR
% Using role type
% Declaring cR:(a->(a->Prop))
% FOF formula (<kernel.Constant object at 0x1b03560>, <kernel.DependentProduct object at 0x1b77b90>) of role type named cS
% Using role type
% Declaring cS:(b->(b->Prop))
% FOF formula (((and ((and (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))) ((ex (a->(b->Prop))) (fun (Xf:(a->(b->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xf Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((Xf Xx) Xy1)) ((Xf Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((Xf Xx1) Xy)) ((Xf Xx2) Xy))->((cR Xx1) Xx2)))))))->((ex (b->(a->Prop))) (fun (Xg:(b->(a->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xg Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((Xg Xy) Xx1)) ((Xg Xy) Xx2))->((cR Xx1) Xx2))))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> ((Xg Xy) Xx)))))))) of role conjecture named cTHM552_pme
% Conjecture to prove = (((and ((and (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))) ((ex (a->(b->Prop))) (fun (Xf:(a->(b->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xf Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((Xf Xx) Xy1)) ((Xf Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((Xf Xx1) Xy)) ((Xf Xx2) Xy))->((cR Xx1) Xx2)))))))->((ex (b->(a->Prop))) (fun (Xg:(b->(a->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xg Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((Xg Xy) Xx1)) ((Xg Xy) Xx2))->((cR Xx1) Xx2))))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> ((Xg Xy) Xx)))))))):Prop
% Parameter a_DUMMY:a.
% Parameter b_DUMMY:b.
% We need to prove ['(((and ((and (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))) ((ex (a->(b->Prop))) (fun (Xf:(a->(b->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xf Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((Xf Xx) Xy1)) ((Xf Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((Xf Xx1) Xy)) ((Xf Xx2) Xy))->((cR Xx1) Xx2)))))))->((ex (b->(a->Prop))) (fun (Xg:(b->(a->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xg Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((Xg Xy) Xx1)) ((Xg Xy) Xx2))->((cR Xx1) Xx2))))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> ((Xg Xy) Xx))))))))']
% Parameter a:Type.
% Parameter b:Type.
% Parameter cR:(a->(a->Prop)).
% Parameter cS:(b->(b->Prop)).
% Trying to prove (((and ((and (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))) ((ex (a->(b->Prop))) (fun (Xf:(a->(b->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xf Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((Xf Xx) Xy1)) ((Xf Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((Xf Xx1) Xy)) ((Xf Xx2) Xy))->((cR Xx1) Xx2)))))))->((ex (b->(a->Prop))) (fun (Xg:(b->(a->Prop)))=> ((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((Xg Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((Xg Xy) Xx1)) ((Xg Xy) Xx2))->((cR Xx1) Xx2))))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> ((Xg Xy) Xx))))))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x12:b) (x110:a)=> ((x2 x110) x12)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x12:b) (x110:a)=> ((x2 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x12:b) (x110:a)=> ((x2 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x12:b) (x110:a)=> ((x2 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x12:b) (x110:a)=> ((x2 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x10:=(fun (x14:b) (x130:a)=> ((x4 x130) x14)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x4 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x4 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x12:b) (x110:a)=> ((x2 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x7000:=(x700 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x4 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x4 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x3)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x3)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x4 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x4:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x4:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x12:b) (x110:a)=> ((x3 x110) x12)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x4:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x5:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x5) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x6:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x7:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x8:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x5)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x4 Xx) Xy1)) ((x4 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x3)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x3)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x3)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x3)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x2 Xx) Xy1)) ((x2 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x14:b) (x130:a)=> ((x2 x130) x14)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x5 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x14:b) (x130:a)=> ((x3 x130) x14)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->P)))=> (((((and_rect (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))) P) x5) x1)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x4:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x5:((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->P)))=> (((((and_rect (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))) P) x5) x1)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->P)))=> (((((and_rect (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))) P) x5) x0)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x4:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x5:((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->P)))=> (((((and_rect (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))) P) x5) x0)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x6)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x5 Xx) Xy1)) ((x5 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found conj20:=(conj2 ((x4 Xy) Xx2)):(((x4 Xy) Xx1)->(((x4 Xy) Xx2)->((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))))
% Found (conj2 ((x4 Xy) Xx2)) as proof of (((x4 Xy) Xx1)->(((x4 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2)) as proof of (((x4 Xy) Xx1)->(((x4 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2)) as proof of (((x4 Xy) Xx1)->(((x4 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2)) as proof of (((x4 Xy) Xx1)->(((x4 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found (and_rect20 ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found ((and_rect2 ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x4 Xy) Xx1)->(((x4 Xy) Xx2)->P)))=> (((((and_rect ((x4 Xy) Xx1)) ((x4 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x4 Xy) Xx1)->(((x4 Xy) Xx2)->P)))=> (((((and_rect ((x4 Xy) Xx1)) ((x4 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (x3000 (((fun (P:Type) (x5:(((x4 Xy) Xx1)->(((x4 Xy) Xx2)->P)))=> (((((and_rect ((x4 Xy) Xx1)) ((x4 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x4 Xy) Xx1)) ((x4 Xy) Xx2)))) as proof of ((cR Xx1) Xx2)
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect30 (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect3 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of ((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))) as proof of (((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect20 (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect2 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))))
% Found (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))) as proof of ((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))))
% Found (and_rect10 (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((and_rect1 ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((fun (P:Type) (x5:((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->P)))=> (((((and_rect (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))) P) x5) x1)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (fun (x4:((and ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))))=> (((fun (P:Type) (x5:((forall (Xx:a), ((cR Xx) Xx))->((forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))->P)))=> (((((and_rect (forall (Xx:a), ((cR Xx) Xx))) (forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv)))) P) x5) x1)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x5:(forall (Xx:a), ((cR Xx) Xx))) (x6:(forall (Xu:a) (Xv:a) (Xw:a), (((and ((cR Xu) Xw)) ((cR Xv) Xw))->((cR Xu) Xv))))=> (((fun (P:Type) (x7:(((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))->((forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2)))) P) x7) x4)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x7:((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))) (x8:(forall (Xx1:a) (Xx2:a) (Xy:b), (((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))))=> (((fun (P:Type) (x9:((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))->((forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))->P)))=> (((((and_rect (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2)))) P) x9) x7)) ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))) (fun (x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))) (x10:(forall (Xx:a) (Xy1:b) (Xy2:b), (((and ((x3 Xx) Xy1)) ((x3 Xx) Xy2))->((cS Xy1) Xy2))))=> ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)))))))))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x12:=(fun (x16:b) (x150:a)=> ((x4 x150) x16)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))
% Found conj20:=(conj2 ((x0 Xy) Xx2)):(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))))
% Found (conj2 ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found (and_rect20 ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found ((and_rect2 ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (x4000 (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)))) as proof of ((cR Xx1) Xx2)
% Found conj20:=(conj2 ((x2 Xy) Xx2)):(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))))
% Found (conj2 ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found (and_rect20 ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found ((and_rect2 ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->P)))=> (((((and_rect ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->P)))=> (((((and_rect ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (x4000 (((fun (P:Type) (x5:(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->P)))=> (((((and_rect ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)))) as proof of ((cR Xx1) Xx2)
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x10:=(fun (x16:b) (x150:a)=> ((x4 x150) x16)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x12:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x8:=(fun (x16:b) (x150:a)=> ((x4 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xx) Xy))))
% Instantiate: x6:=(fun (x16:b) (x150:a)=> ((x4 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x0:=(fun (x16:b) (x150:a)=> ((x5 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x4:=(fun (x16:b) (x150:a)=> ((x5 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x12:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x12:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x12:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x5 Xx) Xy))))
% Instantiate: x2:=(fun (x16:b) (x150:a)=> ((x5 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x8:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x8 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x10:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x7000:=(x700 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x70:=(x7 Xx0):((ex b) (fun (Xy:b)=> ((x3 Xx0) Xy)))
% Instantiate: x0:=(fun (x11:b) (x100:a)=> ((x3 Xx0) x11)):(b->(a->Prop))
% Found x70:=(x7 Xx0):((ex b) (fun (Xy:b)=> ((x3 Xx0) Xy)))
% Instantiate: x2:=(fun (x11:b) (x100:a)=> ((x3 Xx0) x11)):(b->(a->Prop))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found conj20:=(conj2 ((x0 Xy) Xx2)):(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))))
% Found (conj2 ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found (and_rect20 ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found ((and_rect2 ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (x4000 (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)))) as proof of ((cR Xx1) Xx2)
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found conj20:=(conj2 ((x2 Xy) Xx2)):(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))))
% Found (conj2 ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) as proof of (((x2 Xy) Xx1)->(((x2 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found (and_rect20 ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found ((and_rect2 ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->P)))=> (((((and_rect ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->P)))=> (((((and_rect ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (x4000 (((fun (P:Type) (x5:(((x2 Xy) Xx1)->(((x2 Xy) Xx2)->P)))=> (((((and_rect ((x2 Xy) Xx1)) ((x2 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x2 Xy) Xx1)) ((x2 Xy) Xx2)))) as proof of ((cR Xx1) Xx2)
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x0:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))
% Found x6:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x8:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x6 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))
% Found x7000:=(x700 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x9:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x9 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x7000:=(x700 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x6:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x3 Xx) Xy))))
% Instantiate: x2:=(fun (x16:b) (x150:a)=> ((x3 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))
% Found x7:(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xx) Xy))))
% Instantiate: x4:=(fun (x16:b) (x150:a)=> ((x2 x150) x16)):(b->(a->Prop))
% Found x7 as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x4 Xx1) Xy)) ((x4 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x12 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x12 Xy) Xx1)) ((x12 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x5 Xx1) Xy)) ((x5 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x7000:=(x700 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x700 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x70 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x7 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x7 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x8) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x70:=(x7 Xx0):((ex b) (fun (Xy:b)=> ((x3 Xx0) Xy)))
% Instantiate: x0:=(fun (x11:b) (x100:a)=> ((x3 Xx0) x11)):(b->(a->Prop))
% Found x70:=(x7 Xx0):((ex b) (fun (Xy:b)=> ((x3 Xx0) Xy)))
% Instantiate: x0:=(fun (x11:b) (x100:a)=> ((x3 Xx0) x11)):(b->(a->Prop))
% Found x70:=(x7 Xx0):((ex b) (fun (Xy:b)=> ((x3 Xx0) Xy)))
% Instantiate: x2:=(fun (x11:b) (x100:a)=> ((x3 Xx0) x11)):(b->(a->Prop))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x10 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x10 Xy) Xx1)) ((x10 Xy) Xx2))->((cR Xx1) Xx2))))
% Found conj20:=(conj2 ((x0 Xy) Xx2)):(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))))
% Found (conj2 ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) as proof of (((x0 Xy) Xx1)->(((x0 Xy) Xx2)->((and ((cR Xx1) Xw)) ((cR Xx2) Xw))))
% Found (and_rect20 ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found ((and_rect2 ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2))) as proof of ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))
% Found (x4000 (((fun (P:Type) (x5:(((x0 Xy) Xx1)->(((x0 Xy) Xx2)->P)))=> (((((and_rect ((x0 Xy) Xx1)) ((x0 Xy) Xx2)) P) x5) x00)) ((and ((cR Xx1) Xw)) ((cR Xx2) Xw))) ((conj ((x0 Xy) Xx1)) ((x0 Xy) Xx2)))) as proof of ((cR Xx1) Xx2)
% Found x8000:=(x800 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x8000:=(x800 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x800 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x80 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x8 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x8 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x0 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x0 Xy) Xx1)) ((x0 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2)))) x6) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x8 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x8 Xy) Xx1)) ((x8 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x4 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x3 Xx1) Xy)) ((x3 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2)))) x9) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x2 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x2 Xy) Xx1)) ((x2 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x5000:=(x500 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x500 Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x50 Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x5 Xx1) Xx2) Xy) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))
% Found ((conj10 x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found (((conj1 (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found ((((conj (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2)))) x7) (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x5 Xx1) Xx2) Xy))) as proof of ((and (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((x6 Xy) Xx))))) (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x6 Xy) Xx1)) ((x6 Xy) Xx2))->((cR Xx1) Xx2))))
% Found x6000:=(x600 Xy):(((and ((x2 Xx1) Xy)) ((x2 Xx2) Xy))->((cR Xx1) Xx2))
% Found (x600 Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found ((x60 Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (((x6 Xx1) Xx2) Xy) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2))
% Found (fun (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) ((x4 Xy) Xx2))->((cR Xx1) Xx2)))
% Found (fun (Xy:b) (Xx1:a) (Xx2:a)=> (((x6 Xx1) Xx2) Xy)) as proof of (forall (Xy:b) (Xx1:a) (Xx2:a), (((and ((x4 Xy) Xx1)) (
% EOF
%------------------------------------------------------------------------------