TSTP Solution File: SEV245^6 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV245^6 : TPTP v6.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n190.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 13:33:56 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV245^6 : TPTP v6.1.0. Released v5.1.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n190.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:36:46 CDT 2014
% % CPUTime : 300.02
% 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 0xc5c248>, <kernel.Type object at 0xc5c050>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0xc55680>, <kernel.DependentProduct object at 0xc5ccb0>) of role type named cK
% Using role type
% Declaring cK:((a->Prop)->(a->Prop))
% FOF formula ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))) of role conjecture named cTHM116_2S
% Conjecture to prove = ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx))))']
% Parameter a:Type.
% Parameter cK:((a->Prop)->(a->Prop)).
% Trying to prove ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx))))
% Found x2:(X Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found x4:(X Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found x6:(X Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found x2:(X0 Xx0)
% Found x2 as proof of (X Xx0)
% Found (fun (x2:(X0 Xx0))=> x2) as proof of (X Xx0)
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x4:(X0 Xx0)
% Found x4 as proof of (X Xx0)
% Found (fun (x4:(X0 Xx0))=> x4) as proof of (X Xx0)
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x4:(X0 Xx0)
% Found x4 as proof of (X Xx0)
% Found (fun (x4:(X0 Xx0))=> x4) as proof of (X Xx0)
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of (X Xx0)
% Found (fun (x6:(X0 Xx0))=> x6) as proof of (X Xx0)
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of (X Xx0)
% Found (fun (x6:(X0 Xx0))=> x6) as proof of (X Xx0)
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x4:(X0 Xx0)
% Instantiate: X:=X0:(a->Prop)
% Found (fun (x4:(X0 Xx0))=> x4) as proof of (X Xx0)
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found ((x110 (fun (Xx0:a) (x4:(X0 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found (((x11 X) (fun (Xx0:a) (x4:(X0 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found ((((x1 x2) X) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of (X Xx0)
% Found (fun (x6:(X0 Xx0))=> x6) as proof of (X Xx0)
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x2:(X0 Xx0)
% Instantiate: X0:=(cK x3):(a->Prop)
% Found x2 as proof of (X Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X Xx0)
% Found ((and_rect0 (X Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X Xx0)
% Found x2:(X0 Xx0)
% Found x2 as proof of (X Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X Xx0)
% Found ((and_rect0 (X Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X Xx0)
% Found x2:(X1 Xx0)
% Found x2 as proof of (X0 Xx0)
% Found (fun (x2:(X1 Xx0))=> x2) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x4:(X1 Xx0)
% Found x4 as proof of (X0 Xx0)
% Found (fun (x4:(X1 Xx0))=> x4) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of (X0 Xx0)
% Found (fun (x4:(X1 Xx0))=> x4) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of (X0 Xx0)
% Found (fun (x4:(X1 Xx0))=> x4) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of (X0 Xx0)
% Found (fun (x6:(X1 Xx0))=> x6) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of (X0 Xx0)
% Found (fun (x6:(X1 Xx0))=> x6) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of (X0 Xx0)
% Found (fun (x6:(X1 Xx0))=> x6) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of (X0 Xx0)
% Found (fun (x6:(X1 Xx0))=> x6) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of (X0 Xx0)
% Found (fun (x6:(X1 Xx0))=> x6) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of (X0 Xx0)
% Found (fun (x6:(X1 Xx0))=> x6) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Instantiate: X0:=X1:(a->Prop)
% Found (fun (x4:(X1 Xx0))=> x4) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found ((x120 (fun (Xx0:a) (x4:(X1 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found (((x12 X0) (fun (Xx0:a) (x4:(X1 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found ((((x1 x2) X0) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X0) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Instantiate: X1:=(cK x3):(a->Prop)
% Found x2 as proof of (X0 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X0 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X0 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X0 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found ((and_rect0 (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X0 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Instantiate: X0:=X1:(a->Prop)
% Found (fun (x4:(X1 Xx0))=> x4) as proof of (X0 Xx0)
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->(X0 Xx0))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->(X0 Xx)))
% Found ((x120 (fun (Xx0:a) (x4:(X1 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found (((x12 X0) (fun (Xx0:a) (x4:(X1 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found ((((x1 x2) X0) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X0) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X0) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of (X0 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X0 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X0 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X0 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found ((and_rect0 (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X0 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Instantiate: X1:=(cK x3):(a->Prop)
% Found x2 as proof of (X0 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X0 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X0 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X0 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found ((and_rect0 (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X0 Xx0)
% Found x2:(X1 Xx0)
% Found x2 as proof of (X0 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X0 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X0 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X0 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found ((and_rect0 (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X0 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X0 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X0 Xx0)
% Found x2:(X2 Xx0)
% Found x2 as proof of (X1 Xx0)
% Found (fun (x2:(X2 Xx0))=> x2) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x4:(X2 Xx0)
% Found x4 as proof of (X1 Xx0)
% Found (fun (x4:(X2 Xx0))=> x4) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x4:(X2 Xx0)
% Found x4 as proof of (X1 Xx0)
% Found (fun (x4:(X2 Xx0))=> x4) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x4:(X2 Xx0)
% Found x4 as proof of (X1 Xx0)
% Found (fun (x4:(X2 Xx0))=> x4) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x4:(X2 Xx0)
% Found x4 as proof of (X1 Xx0)
% Found (fun (x4:(X2 Xx0))=> x4) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of (X1 Xx0)
% Found (fun (x6:(X2 Xx0))=> x6) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Instantiate: X1:=X2:(a->Prop)
% Found (fun (x4:(X2 Xx0))=> x4) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found ((x130 (fun (Xx0:a) (x4:(X2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found (((x13 X1) (fun (Xx0:a) (x4:(X2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found ((((x1 x2) X1) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X1) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x2:(X2 Xx0)
% Instantiate: X2:=(cK x3):(a->Prop)
% Found x2 as proof of (X1 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X1 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X1 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X1 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found ((and_rect0 (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X1 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Instantiate: X1:=X2:(a->Prop)
% Found (fun (x4:(X2 Xx0))=> x4) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found ((x130 (fun (Xx0:a) (x4:(X2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found (((x13 X1) (fun (Xx0:a) (x4:(X2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found ((((x1 x2) X1) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X1) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X1) Xx)
% Found x2:(X2 Xx0)
% Found x2 as proof of (X1 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X1 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X1 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X1 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found ((and_rect0 (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X1 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x2:(X2 Xx0)
% Instantiate: X2:=(cK x3):(a->Prop)
% Found x2 as proof of (X1 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X1 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X1 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X1 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found ((and_rect0 (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X1 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Instantiate: X1:=X2:(a->Prop)
% Found (fun (x4:(X2 Xx0))=> x4) as proof of (X1 Xx0)
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->(X1 Xx0))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->(X1 Xx)))
% Found ((x130 (fun (Xx0:a) (x4:(X2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found (((x13 X1) (fun (Xx0:a) (x4:(X2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found ((((x1 x2) X1) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X1) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X1) Xx)
% Found x2:(X2 Xx0)
% Found x2 as proof of (X1 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X1 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X1 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X1 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found ((and_rect0 (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X1 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x2:(X2 Xx0)
% Instantiate: X2:=(cK x3):(a->Prop)
% Found x2 as proof of (X1 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X1 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X1 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X1 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found ((and_rect0 (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X1 Xx0)
% Found x2:(X3 Xx0)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x2:(X3 Xx0))=> x2) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x2:(X2 Xx0)
% Found x2 as proof of (X1 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X1 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X1 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X1 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found ((and_rect0 (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X1 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X1 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X1 Xx0)
% Found x4:(X3 Xx0)
% Found x4 as proof of (X2 Xx0)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x4:(X3 Xx0)
% Found x4 as proof of (X2 Xx0)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x4:(X3 Xx0)
% Found x4 as proof of (X2 Xx0)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x4:(X3 Xx0)
% Found x4 as proof of (X2 Xx0)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x4:(X3 Xx0)
% Found x4 as proof of (X2 Xx0)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Instantiate: X2:=X3:(a->Prop)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found ((x140 (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (((x14 X2) (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X2) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of (X2 Xx0)
% Found (fun (x6:(X3 Xx0))=> x6) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x2:(X3 Xx0)
% Instantiate: X3:=(cK x3):(a->Prop)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Instantiate: X2:=X3:(a->Prop)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found ((x140 (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (((x14 X2) (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X2) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x2:(X3 Xx0)
% Instantiate: X3:=(cK x3):(a->Prop)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Instantiate: X2:=X3:(a->Prop)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found ((x140 (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (((x14 X2) (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X2) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x2:(X3 Xx0)
% Instantiate: X3:=(cK x3):(a->Prop)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Instantiate: X2:=X3:(a->Prop)
% Found (fun (x4:(X3 Xx0))=> x4) as proof of (X2 Xx0)
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->(X2 Xx0))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->(X2 Xx)))
% Found ((x140 (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (((x14 X2) (fun (Xx0:a) (x4:(X3 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X2) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X2) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x2:(X4 Xx0)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x2:(X4 Xx0))=> x2) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x4:(X4 Xx0)
% Found x4 as proof of (X3 Xx0)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x4:(X4 Xx0)
% Found x4 as proof of (X3 Xx0)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x4:(X4 Xx0)
% Found x4 as proof of (X3 Xx0)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x4:(X4 Xx0)
% Found x4 as proof of (X3 Xx0)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x2:(X3 Xx0)
% Instantiate: X3:=(cK x3):(a->Prop)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x4:(X4 Xx0)
% Found x4 as proof of (X3 Xx0)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x4:(X4 Xx0)
% Found x4 as proof of (X3 Xx0)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of (X2 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X2 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X2 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X2 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found ((and_rect0 (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X2 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X2 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X2 Xx0)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Instantiate: X3:=X4:(a->Prop)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found ((x150 (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (((x15 X3) (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X3) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of (X3 Xx0)
% Found (fun (x6:(X4 Xx0))=> x6) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x2:(X4 Xx0)
% Instantiate: X4:=(cK x3):(a->Prop)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Instantiate: X3:=X4:(a->Prop)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found ((x150 (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (((x15 X3) (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X3) Xx)
% Found x2:(X4 Xx0)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x2:(X4 Xx0)
% Instantiate: X4:=(cK x3):(a->Prop)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Instantiate: X3:=X4:(a->Prop)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found ((x150 (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (((x15 X3) (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X3) Xx)
% Found x2:(X4 Xx0)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x2:(X4 Xx0)
% Instantiate: X4:=(cK x3):(a->Prop)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Instantiate: X3:=X4:(a->Prop)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found ((x150 (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (((x15 X3) (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X3) Xx)
% Found x2:(X4 Xx0)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x2:(X4 Xx0)
% Instantiate: X4:=(cK x3):(a->Prop)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x2:(X5 Xx0)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x2:(X5 Xx0))=> x2) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x2:(X4 Xx0)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Instantiate: X3:=X4:(a->Prop)
% Found (fun (x4:(X4 Xx0))=> x4) as proof of (X3 Xx0)
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->(X3 Xx0))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->(X3 Xx)))
% Found ((x150 (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (((x15 X3) (fun (Xx0:a) (x4:(X4 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X3) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X3) Xx)
% Found x4:(X5 Xx0)
% Found x4 as proof of (X4 Xx0)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x4:(X5 Xx0)
% Found x4 as proof of (X4 Xx0)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x4:(X5 Xx0)
% Found x4 as proof of (X4 Xx0)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x4:(X5 Xx0)
% Found x4 as proof of (X4 Xx0)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x4:(X5 Xx0)
% Found x4 as proof of (X4 Xx0)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x4:(X5 Xx0)
% Found x4 as proof of (X4 Xx0)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x4:(X5 Xx0)
% Found x4 as proof of (X4 Xx0)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X5) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X5) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X5) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x4:(X5 Xx0)
% Instantiate: X4:=X5:(a->Prop)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found ((x160 (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (((x16 X4) (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X4) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x6:(X5 Xx0)
% Found x6 as proof of (X4 Xx0)
% Found (fun (x6:(X5 Xx0))=> x6) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% Found x2:(X4 Xx0)
% Instantiate: X4:=(cK x3):(a->Prop)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found x2:(X4 Xx0)
% Found x2 as proof of (X3 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X3 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X3 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X3 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found ((and_rect0 (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X3 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X3 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X3 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x4:(X5 Xx0)
% Instantiate: X4:=X5:(a->Prop)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found ((x160 (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (((x16 X4) (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X4) Xx)
% Found x2:(X5 Xx0)
% Instantiate: X5:=(cK x3):(a->Prop)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x2:(X5 Xx0)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found x2:(X5 Xx0)
% Instantiate: X5:=(cK x3):(a->Prop)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x4:(X5 Xx0)
% Instantiate: X4:=X5:(a->Prop)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found ((x160 (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (((x16 X4) (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X4) Xx)
% Found x2:(X5 Xx0)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found x2:(X5 Xx0)
% Instantiate: X5:=(cK x3):(a->Prop)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x4:(X5 Xx0)
% Instantiate: X4:=X5:(a->Prop)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found ((x160 (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (((x16 X4) (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X4) Xx)
% Found x2:(X5 Xx0)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found x2:(X5 Xx0)
% Instantiate: X5:=(cK x3):(a->Prop)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x4:(X5 Xx0)
% Instantiate: X4:=X5:(a->Prop)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found ((x160 (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (((x16 X4) (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X4) Xx)
% Found x2:(X5 Xx0)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x2:(X6 Xx0))=> x2) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x2:(X5 Xx0)
% Instantiate: X5:=(cK x3):(a->Prop)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x4:(X6 Xx0)
% Found x4 as proof of (X5 Xx0)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X6) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X6) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X6) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x2:(X5 Xx0)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found x4:(X5 Xx0)
% Instantiate: X4:=X5:(a->Prop)
% Found (fun (x4:(X5 Xx0))=> x4) as proof of (X4 Xx0)
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->(X4 Xx0))
% Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->(X4 Xx)))
% Found ((x160 (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (((x16 X4) (fun (Xx0:a) (x4:(X5 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X4) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X4) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x4:(X6 Xx0)
% Instantiate: X5:=X6:(a->Prop)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found ((x170 (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (((x17 X5) (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X5) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x6:(X6 Xx0)
% Found x6 as proof of (X5 Xx0)
% Found (fun (x6:(X6 Xx0))=> x6) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x4:(X6 Xx0)
% Instantiate: X5:=X6:(a->Prop)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found ((x170 (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (((x17 X5) (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X5) Xx)
% Found x2:(X6 Xx0)
% Instantiate: X6:=(cK x3):(a->Prop)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x2:(X5 Xx0)
% Instantiate: X5:=(cK x3):(a->Prop)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x2:(X5 Xx0)
% Found x2 as proof of (X4 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X4 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X4 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X4 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found ((and_rect0 (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X4 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X4 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X4 Xx0)
% Found x2:(X6 Xx0)
% Instantiate: X6:=(cK x3):(a->Prop)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x4:(X6 Xx0)
% Instantiate: X5:=X6:(a->Prop)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found ((x170 (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (((x17 X5) (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X5) Xx)
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x2:(X6 Xx0)
% Instantiate: X6:=(cK x3):(a->Prop)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x4:(X6 Xx0)
% Instantiate: X5:=X6:(a->Prop)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found ((x170 (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (((x17 X5) (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X5) Xx)
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x2:(X6 Xx0)
% Instantiate: X6:=(cK x3):(a->Prop)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x4:(X6 Xx0)
% Instantiate: X5:=X6:(a->Prop)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found ((x170 (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (((x17 X5) (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X5) Xx)
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x2:(X6 Xx0)
% Instantiate: X6:=(cK x3):(a->Prop)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x2:(X7 Xx0))=> x2) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x2:(X7 Xx0))=> x2) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x2:(X7 Xx0))=> x2) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x4:(X6 Xx0)
% Instantiate: X5:=X6:(a->Prop)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found ((x170 (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (((x17 X5) (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X5) Xx)
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Found x4 as proof of (X6 Xx0)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X7) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X7) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X7) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x6:(X7 Xx0)
% Found x6 as proof of (X6 Xx0)
% Found (fun (x6:(X7 Xx0))=> x6) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x6:(X7 Xx0))=> x6) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X7) Xx)
% Found x2:(X6 Xx0)
% Instantiate: X6:=(cK x3):(a->Prop)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found x4:(X6 Xx0)
% Instantiate: X5:=X6:(a->Prop)
% Found (fun (x4:(X6 Xx0))=> x4) as proof of (X5 Xx0)
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->(X5 Xx0))
% Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->(X5 Xx)))
% Found ((x170 (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (((x17 X5) (fun (Xx0:a) (x4:(X6 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X5) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X5) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x2:(X6 Xx0)
% Instantiate: X6:=(cK x3):(a->Prop)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x2:(X6 Xx0)
% Found x2 as proof of (X5 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X5 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X5 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X5 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found ((and_rect0 (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X5 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X5 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X5 Xx0)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x2:(X8 Xx0))=> x2) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x2:(X8 Xx0))=> x2) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x2:(X8 Xx0))=> x2) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Found x4 as proof of (X7 Xx0)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X8) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X8) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X8) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x6:(X8 Xx0)
% Found x6 as proof of (X7 Xx0)
% Found (fun (x6:(X8 Xx0))=> x6) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x6:(X8 Xx0))=> x6) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found x4:(X7 Xx0)
% Instantiate: X6:=X7:(a->Prop)
% Found (fun (x4:(X7 Xx0))=> x4) as proof of (X6 Xx0)
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of ((X7 Xx0)->(X6 Xx0))
% Found (fun (Xx0:a) (x4:(X7 Xx0))=> x4) as proof of (forall (Xx:a), ((X7 Xx)->(X6 Xx)))
% Found ((x180 (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (((x18 X6) (fun (Xx0:a) (x4:(X7 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X6) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X6) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X6) Xx)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X7) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X7) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found ((and_rect0 ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X7) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x2:(X7 Xx0)
% Instantiate: X7:=(cK x3):(a->Prop)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x2:(X7 Xx0)
% Found x2 as proof of (X6 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X6 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X6 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X6 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found ((and_rect0 (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X6 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X6 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X6 Xx0)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x2:(X9 Xx0))=> x2) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x2:(X9 Xx0))=> x2) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x2:(X9 Xx0))=> x2) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Found x4 as proof of (X8 Xx0)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X9) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X9) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X9) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x6:(X9 Xx0)
% Found x6 as proof of (X8 Xx0)
% Found (fun (x6:(X9 Xx0))=> x6) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x6:(X9 Xx0))=> x6) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found x4:(X8 Xx0)
% Instantiate: X7:=X8:(a->Prop)
% Found (fun (x4:(X8 Xx0))=> x4) as proof of (X7 Xx0)
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of ((X8 Xx0)->(X7 Xx0))
% Found (fun (Xx0:a) (x4:(X8 Xx0))=> x4) as proof of (forall (Xx:a), ((X8 Xx)->(X7 Xx)))
% Found ((x190 (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (((x19 X7) (fun (Xx0:a) (x4:(X8 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X7) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X7) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X7) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X8) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X8) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found ((and_rect0 ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X8) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x2:(X8 Xx0)
% Instantiate: X8:=(cK x3):(a->Prop)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x2:(X8 Xx0)
% Found x2 as proof of (X7 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X7 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X7 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X7 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found ((and_rect0 (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X7 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X7 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X7 Xx0)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x2:(X10 Xx0)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x2:(X10 Xx0))=> x2) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x2:(X10 Xx0))=> x2) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x2:(X10 Xx0))=> x2) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Found x4 as proof of (X9 Xx0)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X10) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X10) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X10) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Instantiate: X9:=X10:(a->Prop)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found ((x1120 (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (((x112 X9) (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X9) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x6:(X10 Xx0)
% Found x6 as proof of (X9 Xx0)
% Found (fun (x6:(X10 Xx0))=> x6) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x6:(X10 Xx0))=> x6) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X10) Xx)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Instantiate: X9:=X10:(a->Prop)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found ((x1120 (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (((x112 X9) (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X9) Xx)
% Found x2:(X10 Xx0)
% Instantiate: X10:=(cK x3):(a->Prop)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x2:(X10 Xx0)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X10) Xx)
% Found x2:(X10 Xx0)
% Instantiate: X10:=(cK x3):(a->Prop)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Instantiate: X9:=X10:(a->Prop)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found ((x1120 (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (((x112 X9) (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X9) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x2:(X10 Xx0)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X10) Xx)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x2:(X10 Xx0)
% Instantiate: X10:=(cK x3):(a->Prop)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Instantiate: X9:=X10:(a->Prop)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found ((x1120 (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (((x112 X9) (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X9) Xx)
% Found x2:(X10 Xx0)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X10) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x2:(X10 Xx0)
% Instantiate: X10:=(cK x3):(a->Prop)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Instantiate: X9:=X10:(a->Prop)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found ((x1120 (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (((x112 X9) (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X9) Xx)
% Found x2:(X10 Xx0)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found x4:(X9 Xx0)
% Instantiate: X8:=X9:(a->Prop)
% Found (fun (x4:(X9 Xx0))=> x4) as proof of (X8 Xx0)
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of ((X9 Xx0)->(X8 Xx0))
% Found (fun (Xx0:a) (x4:(X9 Xx0))=> x4) as proof of (forall (Xx:a), ((X9 Xx)->(X8 Xx)))
% Found ((x1110 (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (((x111 X8) (fun (Xx0:a) (x4:(X9 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X8) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X8) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X8) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X10) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X9) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X9) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found ((and_rect0 ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X9) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found x2:(X10 Xx0)
% Instantiate: X10:=(cK x3):(a->Prop)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Instantiate: X9:=X10:(a->Prop)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found ((x1120 (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (((x112 X9) (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) X9) (fun (Xx0:a) (x4:(x2 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK x2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))))) as proof of ((cK X9) Xx)
% Found x2:(X10 Xx0)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X10) Xx)
% Found x2:(X9 Xx0)
% Instantiate: X9:=(cK x3):(a->Prop)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x2:(X9 Xx0)
% Found x2 as proof of (X8 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X8 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X8 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X8 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found ((and_rect0 (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X8 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X8 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X8 Xx0)
% Found x2:(X10 Xx0)
% Instantiate: X10:=(cK x3):(a->Prop)
% Found x2 as proof of (X9 Xx0)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (X9 Xx0)
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(X9 Xx0))
% Found (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->(X9 Xx0)))
% Found (and_rect00 (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found ((and_rect0 (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (X9 Xx0)
% Found (fun (x4:((and (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x3 Xx)) P) x5) x4)) (X9 Xx0)) (fun (x5:(forall (Xx00:a), ((x3 Xx00)->((cK x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (X9 Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X10) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X10) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found ((and_rect0 ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X10) Xx)
% Found x4:(X10 Xx0)
% Instantiate: X9:=X10:(a->Prop)
% Found (fun (x4:(X10 Xx0))=> x4) as proof of (X9 Xx0)
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of ((X10 Xx0)->(X9 Xx0))
% Found (fun (Xx0:a) (x4:(X10 Xx0))=> x4) as proof of (forall (Xx:a), ((X10 Xx)->(X9 Xx)))
% Found ((x1120 (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found (((x112 X9) (fun (Xx0:a) (x4:(X10 Xx0))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X10) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X9) Xx)
% Found ((((x1 x2) X9) (fun (X
% EOF
%------------------------------------------------------------------------------